Although there are several chemicals that MIGHT be used, most people don't need them all.
Bleach for chlorination
Muriatic Acid to lower pH (and to lower TA, but it's more complex than just adding it)
Baking Soda to raise TA
Borax to raise pH
Washing Soda to raise pH
Cyanuric Acid also known as CYA or stabilizer to stabilize chlorine
These are the primary items to have on hand. I never use baking soda, washing soda or borax because my water is high alkalinity, so the pH always climbs.
As to what you need, get a sample of your fill water tested, preferably by yourself with the HTH 6way kit you can get at Walmart to find out where you stand on pH and alkalinity. Find out how much water your pool holds when full to the skimmer line to base your calculations on. You'll probably have to buy quite a bit more CYA than you need, but it keeps. Tell us about your pool and fill water and we can give you better guesses as to what you'll need.
