What would be a good assassin build?

search "assassin" in the field near top right of the screen. There are about a jillion posts concerning this.

stealth level 100..

one handed, archery, alchemy, sneak, light armour.

For the look go with Riften guard armour and Alik'r hood. Looks better than the DB ninja crap.

Here's my recommendation: http://skyrimcalculator.com/#77828

Focuses on Archery and Poisons, while still giving you the option of backstabbing for insane damage plus the "poisoner" perk in pick pocketing which adds a whole new element. For a fun factor I didn't perk out armor-- so if you play on Master you have two options: Stay in the shadows or die. For RP purposes I'd say no magic at all-- be it perks or anything else.

Assassin. So I'm assuming you don't want the pick pocketing skills that remove weapons and armor? I thought that was a load of fun.

I guess you would need smithing, enchanting, and alchemy to boost your blacksmithing skill to +32% per clothing compatible with the enchantment, and then sharpen your daggers and bows to deal maximum damage per hit. This would be result in many one shot kills, like an assassin should.

So, you would need to work on one handed perks to increase dagger damage as well as dual wielding speeds, etc. archery is another obvious choice.

I think questions like these are very self explanatory. It's not hard to figure out. If you think you'll need it, you probably will.
Another thing you'll probably want is illusion skills. This is actually very important for an interesting gameplay if you want options that enhance your stealth capabilities. That said, you should probably become a vampire. A full fledged vampire.

My Assassin had Sneak, Light Armour, One-Handed, Archery, Smithing and Enchanting. You can choose whether you want either One-Handed or Archery, or you can pick both. Smithing and Enchanting are there if you want to make yourself stronger, so that depends on your difficulty level. You can expand the build with Illusion, allowing you to Calm opponents once they detect you, or set 'em up against each other with Frenzy.

I am on my third Assassin character. I like the Vampire for this, because they improve Illusion and Sneak. They are two very key Assassin skills. IMO. I also like to get creative about the kills. So Alchemy comes into play with poisons. Then you need Pickpocket to slip the poisons. Other methods of delivery would be by Bow or Melee. Being an Alchemist, you can create a potion to boost ANY skill like Archery or 1H. This will support the delivery system.

There are many different ways to play an Assassin, pending your playstyle and RP.

TBH, once you reach very high levels of sneak and get the "Shadow warrior" perk, you won't even really need illusion anymore.