I have a certain idea about how my Bosmer will be as a person, but I need help to create the ultimate combo of skills to fit the type. I'm uncertain at the point if I will make a female or male Bosmer, but what I know is that I will live in Riften or somewhere close to the Rift hold (alchemist shack?)

My main skill will be alchemy, but the other skills is something i need help with. All my characters, except one has light armor as a skill, all my characters has one-handed as a skill as well. I need something creative and I need it to fit to the alchemist vocation so i can't be wearing heavy armor and a claymore. This character will be devoted to gain lvl 100 in alchemy so the skills has to fit the Bosmer (and take in mind that the skill has to somewhat suit a Bosmer as well).
Help me out and be creative as I've almost tried every kind of Thief/Mage class there is (which and alchemist is) so this one needs to be special and if you like, please add a story or explain the combo's you've chosen.

Well, I have a few skills I can recomend to the character¨; Sneak and Speech(buying all those ingredients is expensive). You should, in my opinion, go with clothes if you want an alchemist and maybe add some enchanting to it. Carry a dagger, but don't use one-handed as a major skill; use it to deliever the poisons.

Just my two scents.

Well, if you want to focus mainly on alchemy, then I'd recommend making it the very epitome of your character and incorporate it even into the backstory of your character itself. I, at one point in time, was going to make a build like this. Your guy could have fled his homeland, for any particular reason of your choice, and has since been living in the various wilds of Tamriel. Because of this, he has developed an ability to heal himself using natural ingredients he has access to and is a skilled alchemist. As for other skills, I simply have to recommend archery as the Bosmer are well known to be the finest archers in all of Tamriel. Light armour is really your only option for this type of character as far as that goes, however. That is, unless you want a challenge to play through the game wearing regular clothes (which offer no armour rating at all).

EDIT: Whoever is above me, they beat me to it! But, yes, wear regular clothes for a nice change. Speech is also useful for almost all character builds simply to get better prices.

Well if youre going for ranged combat why not some archery, i mean it may become bland to always use it so maybe it could be a "if a opportunity raises" sort of thing but i mean its a Bosmer their practically born with a bow.... Ninjad I hate you... jk

Why don't you make a build concentrated to supporting your follower? An Alchemist, who just wants to collect ingredients while his faithful warrior companion keeps him safe - and when it comes to the battle, our good Bosmer keep him alive healing him, and occasionally dealing damage from the back row as an archer.

By doing that, your main pillars will be:
- Alchemy: do potions for her / him too, I don't know how many they'll use from them, but a Recover Health potion always comes handy
- Restoration: plan B and your best friend at the same time, healing him / her directly is the most safe solution.
- Weapons: bounded or lore-friendly bow, since Bosmers are the best archers in Skyrim. Dagger as backup, and remember: use your own poisons!
- Money: indeed, you won't have financial problems as an alchemist, so you can buy the finest things for you and your follower

As for gear, I would stick to simple boots and robes, maybe Monk or Blue Robes, or to a simple cloth with visible belts.
If you want to enchant as well, you know what to do - but beware, those two can easily make you god-like in a second!

-Destruction: Except say it results from chemical reactions instead of magicka. Only use fire and frost spells to demonstrate explosions, reactions that flash freeze the enemy, and shooting flames from your hands using a greek fire kind of compound. No runes and no perks(you will also need to use potions of fortify destruction to simulate the powering of your "spells").
-Alteration: To give your class armor in the early game.
-one-handed: To give you a viable delivery system for poisons, maybe taking armsman but skipping power attack and dual wield perks.
-Enchant: To give your clothes a buff to potion making or something more combat oriented.

Also, creating restore health potion with other benefits will let your companions take advantage of the secondary effect and give them a helpful buff hopefully.