Choose lightweight equipment so you can carry it round with you.
Go to the clothes shop in Solitude for a full range of dresswear to choose from, including gloves and circlets and hats.
Saving your coins is irrelevant.
Most clothing costs less than a single petty soul gem.
edit:
Following on from a good point about naming: you can use a ".
" full-stop at the start of the name.
All symbols are place in the inventory first.
I have mine named like: .Alchemist's Cowl .Alchemist's Safety Gloves .Forgemaster's
Ovenmitts .Forgemaster's Heatproof Apron etc...
gaming.stackexchange.com/users/16559/Asdafgh
I just want to add to the other comments, be sure to name them otherwise things get really confusing.
And don't name them hat of alchemy.
Name it Alchemy hat, alchemy gloves,
alchemy amulet etc so that when you equip them they're all in the same place.
I wish I could name potions.
Try my potion generator .
gaming.stackexchange.com/users/16218/Jimmy Ruska
Enchantments in Skyrim are the same, no matter what item you put them on (for a given skill level, soul size, and perks known).
This means enchanting a pair of Leather Bracers with "Fortify Smithing" is just as effective as enchanting a pair of Daedric Gauntlets with the same effect.
This is different from Oblivion, where item choice mattered, mostly because many pieces of clothing took up multiple "slots" on the character's body, and if you weren't careful, you could wind up with fewer enchants than if you had worn armor.
gaming.stackexchange.com/users/336/Raven Dreamer
If you don't mind abusing a glitch, you can wear a circlet and a forsworn helmet simultaneously, granting you 5 total items boosting your alchemy stat.
Sadly, not possible with the chef hat :(
gaming.stackexchange.com/users/16775/Dan
4 items in apparel for alchemy-i personally use... gloves -weight .5
hat
-weight .5 ring
-weight .3 necklace-weight .5
now i have all these items Dual enchanted 30% Smithing/Alchemy " all except the Hat which won't take smithing,i singled with Alchemy and added smithingto my normal armor along with magika regeneration "saving money by Dual enchanting-saving weight by using the items i listed above.the price of the item from the crappiest ring to the most expensive sadly has notbeneficial effect.hoped this helped
gaming.stackexchange.com/users/15734/2 SCooPS
You can obtain the Krosis mask at Shearpoint, which adds 20 points to alchemy when worn.
Combined with the other alchemy-enchanted apparel that you've made, you can make the strongest enchanting potion in the game to create more powerful alchemy apparel.
After donning these and the Krosis mask, make even stronger enchanting potions, which can be used to to create even stronger alchemy apparel and so on until you achieve extraordinarily high level enchanting potions, way stronger than the game gifts you.
You have to keep changing into the ever more powerful alchemy apparel to keep upping the enchanting potion.
Then use your ultra powerful enchanting potions to make smithing apparel that can be worn to improve armour and weapons 1000%+ when you go smithing.
You basically become invincible, but I would caution that the game becomes less interesting when there's no challenge.
Don't give Krosis to your familiar to carry for you.
There is a bug where the item could disappear from their inventory.
And don't sell it if you want to exploit the alchemy/enchanting loop.
You need it to do that.
It's possible to buy it back from the merchant you sold it to, or pickpocket it if you can't see it in their inventory during trade.
But you have to remember who you sold it to!
I forgot. :-(
gaming.stackexchange.com/users/62285/Vadel
How can I save my coins when enchanting with the fortify alchemy spell as described  here ? Does it make sense to use light leather clothes?
What are the recomended clothes to use with fortify alchemy?
gaming.stackexchange.com
<the-elder-scrolls-5-skyrim>
gaming.stackexchange.com/questions/42207
gaming.stackexchange.com/users/13634/Gigamegs
Choose lightweight equipment you can carry round with you. It seems that while it is a complicated matter, the general rule is to use gear identified as lightweight.
Recommended clothers to wear, regarding fortify alchemy.