Wanting to play something other then a warrior, I want to try a Dunmer Assassin. To do this, I will use One Handed, Light Armor, Sneak, Archery, Illusion, Alteration, Alchemy, and maybe Pocketpicking as my skills. To make each of my skills efficient, I've figured which perks to take and which not to.
One Handed - Armsman (5), Dual Fury (2), and Dual Savagery.
Light Armor - 0 Due to the fact, I'll be sneaking the whole time and I'll be using Alteration spells to boost up my armor rating.
Sneak - Max of every perk.
Archery - Overdraw (5), Eagle Eye, Steady Hand (2), and maybe Power Shot (could use poisons to paralyze).
Illusion - Novice, Animage, Apprentice. Kindred Mage, Adept, and Quiet Casting.
Alteration - Novice , Apprentice ,Magic Resistance (3), Adept, and Stability.
Alchemy - Alchemist (5), Physician, Poisoner, Concentrated Poison, Green Thumb, and Snakeblood.
Pocketpicking - Light Fingers (5), Night Thief, and Poisoned
Now with the perks out of the way, I need to figure out how to distribute stats. This is were you guys come in along with advice and tweaking of my build.
I'll start with the perks and then go to what I personally used for my stat boosts... This is also based on nearly 200 hours of play and and I'm now level 81 but I will only go through what I use for assassination here instead of my complete Jack of All Trades style build... Also I play on Master difficulty and still have the ability to one shot Giants and even took out an Ancient Dragon on Master with my pair of Daedric Daggers (Legendary though far beyond the normal legendary level) doing 112 damage each with all my perks and a pair of shrouded gloves (total base damage out of this is 6720)...
First of all in the One Handed perks there's another that can be useful but you don't technically need, it's called Fighting Stance and will reduce the cost of your power attacks with one handed weapons by 25%
Light Armor- I recommend simply because no matter how good you are there's always a chance that you will have to fight things without the aid of sneaking around, but I only took the all of the perks EXCEPT Deft Movement, I simply don't want to rely on luck to save my skin once in a while...
Sneak- First of all I manage to sneak by anything just fine with only the first rank in the Stealth perk so I find the extra ranks in it useless which saves you 4 extra perk points you can better place elsewhere... Take the backstabbing branch all the way up to Assassins Blade for the 15x sneak attack damage with daggers... Deadly aim has its uses too since there are times you will want to use a bow to kill your enemy from afar however it isn't nearly as deadly as your daggers so use those if at all possible... Now for the other branch, Muffled Movement is only necessary because it's required for Light Foot, which is one of the more useful stealth perks but I personally won't go past it since I've got no use for Silent Roll and once you have an enchanting ability Silence will also be obsolete (Until you have a Muffle enchantment on your boots you can just use the spell of the same name and not have an issue as long as you have Quiet Casting but more on that when we get there) with the proper gear and spells...
Archery- All ranks of Overdraw are a must for ranged sneak attacks since your bow won't come close to the daggers and only gets a 3x sneak attack bonus... Critical shot isn't that good unless you want to rely on luck and as an assassin that's usually not the best idea so I would avoid it unless you want perks that require you to have it... Eagle Eye will allow you to easier take out targets from a safer distance so it's another excellent skill to have... Steady Hand has it's uses but I only use it when fighting dragons so you don't have to have it... Power Shot is actually useful since it's percentage is 50% and I find it comes in handy but mainly only has use on assassinations where you take out an enemy where there is noone that can witness it anyway so it's not required... Quick Shot is also good but is another one where you'll only get any real use out of it when fighting dragons or when you can't kill the enemy in a single shot... And Bullseye is another luck based perk that I have but is only useful if you get lucky with a shot that doesn't kill the enemy so it's another one that's not necessary...
Illusion- Those who play assassins that overlook this tree are foolish in my honest opinion, 1 main reason INVISIBILITY... First of all take all the spell level perks through Expert but not to Master... None of the Master level spells are that useful unless you have ALL of the Illusion perks and if you need to cast Harmony you've done something extremely wrong and also unless you have some serious casting cost enchantments on your armor for Illusion magic then it's going to cost more mana than you are likely to have at any given time unless you focus relatively heavily in it... At 100 Illusion with all perks up to expert the Invisibility spell will cost you 99 mana to use and with the armor setup like I've got with -28% casting cost for Illusion it only costs me ~73 mana... Muffle is good until you get the Enchantment on your boots... For the other perks go all the way up to quiet casting through the Kindred Mage and Animage perks and I also have Master of the Mind and find it useful but much less so than the other perks I've listed... None of the calm, frenzy or fear spells have any worthwhile use as an assassin because, as I've mentioned previously, if you have a need for them you've done something wrong (though I will admit that Mayhem can be quite entertaining at times to cause some serious chaos)... Muffle is also, for some odd reason, the fastest way to raise your Illusion skill to max or at least high enough to use invisibility but at some point you will want to max it if for nothing else but the reduced casting cost of your spells that comes from the higher levels in the skill...
Alteration- I find that this school, while it does have its uses, has no requirement for perks in it since there are only three spells in it that I've found to be truly useful (Candle Light, Mage Light and Telekinesis) and I have and have tested every single spell in the game but I don't have perks in all the skills because I found them to not be very useful... As far as the three spells go Candle Light is useful for lighting your way when you have a need for it but you won't want to use it often since for assassinations only the Falmer won't see you with it up as they are blind, for Mage Light it's the same basic concept but it doesn't follow you around and instead it goes where you aim the spell, Telekinesis on the other hand is the only of these three spells that costs much mana but you'll pretty much only use it for disabling traps before you get to them or picking up items from trapped objects so you won't need to worry about its high cost... Detect Life and Detect Undead can also be extremely useful at times when planing your path before making your kill but again you won't need to use them for very long and with quiet casting you don't have to worry about your distance from the enemies too much...
Alchemy- While Alchemy has its uses I don't find the perks in it to be that useful since the only thing I've ever made with it that I used were a couple of invisibility potions for the times when the spell isn't fast enough for my needs, and these times are few and far between... If you find that you still want to use it for poisons that's up to you but I would recommend the Purity perk when you hit 100 in the skill so you don't give any of your opponents any bonuses with the poisons or yourself any negatives out of the potions...
Pickpocketing- The only perks in this I've actually gotten much use out of aren't really assassin based but Stealing people's weapons an armor off of them before you stab them can be quite entertaining but you still have to find a Fence to sell the armor too unless you have a high level of Speechcraft with the right perks... Poisoned could have it's uses but I've never actually found it to be worth it, but then again I also prefer the more personal feel of a knife in the back when killing stealthily so if you want it take it but otherwise I'd just leave it out... And for the rest of the perks Extra Pockets is good for anyone and you don't need 5 ranks in Light Fingers to steal most things and pretty much any higer level items that are useful are not going to be obtainable through picking pockets...
Now for other skills that have excellent uses for an assassin...
First of these is Enchanting- Enchanting will allow you to put your own enchantments on your armor and if you take all of the perks from both of the branches on the right side and middle then you will be able to enchant each of your weapons and armor along with your rings and amulets with 2 enchantments each with no penalties thus making you even more powerful... All 5 levels of the Enchanter perk and have enhanced skill enchantments and thus enchant armor pieces with 25% bonuses for smithing without a potion to enhance it and if you buy a potion (Elixir of Enchanting at the highest level for this) to enhance it then you can get this to 28% and thus make your weapons and armor even more powerful... This is how I've got 1025 armor with full Dragon Scale and weapons that do so much damage... Also putting a Muffle enchantment on your boots solves the need for any spell but invisibility for assassination...
Next of these is Smithing and if you are making your own armor you'll want at least up to glass armor though I wear Dragon Scale for aesthetics... Once Smithing is at 100 you can upgrade your weapons and armor to extremely high levels... With all perks my Daedric Daggers do 112 damage each plus enchantments and my Daedric Swords do 250 each with all perks my Daedric Bow is around 225 I believe with all perks but I'm not sure on the bow since I don't use it as often... Smithing is the only way to obtain Daedric weapons in the game as noone carries them and you will definitely WANT them though they aren't required... Unfortunately aside from Arcane Blacksmith as a light armor user who uses weapons as your main source of damage this means you're going to need all perks in this set if you want the best armor you can get though you won't actually need it since you can easily achieve the armor cap which is just below 600 without Dragon Scale armor or even Glass...
Lockpicking- Pretty much a requirement since they've removed the unlock spells from previous games, and you WILL have to break into places if you follow the Dark Brotherhood quest line (besides that who wants to pass up a chest filled with loot because they couldn't pick the lock?), but if you simply invest perk points at each level up to expert and then take Locksmith and Unbreakable you'll have a Skeleton Key in every pick... Quick hands is also good if you want it but wax key is the most useless perk ever since once you've picked the lock I've never seen one become relocked that I would have any need to go back into... Master Locks is useless though since if you take unbreakable you won't have a use for Master level locks to be easier since you'll never break a pick again...
Destruction- Destruction is only useful for some amusemant if you want to use the traps from it but it takes forever to train Destruction and it's not really worth it unless you fancy yourself to be a Wizard style Assassin...
Now for the attributes...
I would recommend 50% of your levels stat increases to go to health and 30% to go into Mana (Magicka) with the last 20% being placed in stamina to be able to power attack more often if you are in real combat (which won't be often, I can clear most dungeons without ever being seen)... Invisibility is expensive but if you have enough mana it will regenerate faster than you will need it out of combat and with quiet casting you can recast it right in front of someone without them noticing you unless it wore off on its own...
For proper use of invisibility when you have to kill multiple targets and want to use it the best way is to have one dagger in your right hand and invisibility prepped in your left hand and already starting to cast (i.e. you have the casting button held down but haven't released the button yet) and don't release the casting button until after the animation for the attack finishes so that it goes off properly, for some reason if you let go of the spell before the attack animation is finished it won't cast either due to a bug or for balance, I don't know which...
Restoration- Though I don't actually see the need to invest perk points into this school of magic it definitely has its uses with healing spells and such...
These are only my opinions based on how I play and my own experiences but I hope they help... Feel free to do as you will with my advice as that is all it is, advice... This is by no means how you have to build your character, it's just how I recommend to do so...