Most of you know a lot of this already, but I wanted to have it all in one place. If anyone has more info to add, let me know and I will post it.
Race
Altmer: Alchemy synergizes well with many of the magic skills
Argonian: With the water breathing ability, Argonians are experts at finding underwater ingredients.
Bosmer: Maybe the best choice. Natural alchemy ability and 50% poison resistance with snake blood gives you 100% poison resistance.
Breton: Natural alchemy ability and potions can enhance magic resistance.
Dunmer: Probably good at making poisons
Imperial: Not the most likely race.
Khajiit: Alchemy ability, and good at finding (stealing) ingredients.
Nord: Could be role-played as a someone who has knowledge of all the plants and animals of Skyrim
Orc: Not the most likely race.
Redguard: 50% poison resistance with snake blood equals 100% poison resistance.
House: Windstad Manor with greenhouse and fish hatchery
Synergies with other skills
Combat (Archery, One-handed and Two-handed, Block)
Alchemy can make a huge boost to weapon damage as well as applying poisons. I personally think Alchemy has a special synergy with Two-handed. when using two-handed weapons you need a way to heal, and alchemy may be a better choice than restoration because there’s no need to put down your weapon. Also the sweep perk in two-handed allows the poison to be used on all enemies that are hit. Combined with Concentrated Poison could be quite devastating.
Armor (Light and Heavy)
Smithing and Enchanting
Magic
Alteration: Potions of alteration extend the duration of spells. This can be awesome when combined with paralyze and Dragonhide. Dragonhide can be viable for longer battles when combined with a fortify alteration potion.
Conjuration: Alchemy makes these spells last longer.
Illusion: Potions increase the power of illusion spells but are applied before perks. If you are already fully perked in illusion, you may not need alchemy to boost it.
Restoration: Actually haven’t tested this too much, but am interested to know what potions do to wards, protection, and turn undead spells.
Staves and scrolls: Fortify potions effect staves and scrolls.The Sanguine Rose plus Fortify conjuration Potion can be a good replacement most of the conjuration tree. All destruction staves, scrolls and paralysis staff are effected. Those blizzard scrolls you find can be devastating when combined with a potion.
Stealth
Speech: Speech and alchemy have great synergy. Fortify barter potions make you rich. the Merchant perk is very important as you can sell potions to anyone, and it unlocks rare ingredients that merchants normally don’t sell. All my alchemy characters take the merchant perk.
From a post by abacus707, here is a list of potions that a great alchemist can make:
+100 Fortify Health
+100 fortify stamina
+75% resist fire, resist frost, resist shock
+25% resist magic
+150% regenerate magicka
+150% regenerate health
+150% regenerate stamina
+150% fortify one-handed
+150% fortify two-handed
+150% fortify archery
+150% fortify smithing
+150% fortify lockpicking
+150% fortify pickpocketing
+150% fortify sneak