What potions can my followers use?

This source claims that followers will drink potions, but not ones that you've made: http://www.gamefaqs.com/boards/615803-the-elder-scrolls-v-skyrim/61334541/682887748

This source has evidence that followers use healing potions and they also claim to have seen a potion being consumed animation: http://www.uesp.net/wiki/Skyrim_talk:Followers#Healing_Potions

Since there is evidence that followers have weapon preferences and combat styles, it stands to reason that they may have a potion preference also. (I cannot confirm this yet.)

A simple test, give your follower some store bought potions and take them to a bandit camp. See what happens.

I've found that if you do any kind of trade, the follower tends to equip their preferred gear. Hard to say how that would affect potion use.