Lydia is the best for this. She's always upbeat and happy till you try to give her an entire suit of hand made armor and weapons and she's all like "Great... I'll carry all YOUR burdens..." Missy, I'm giving you good stuff here!
I do wish there was a method of telling the companion what to actually use. Or even seeing what they are using. I gave her a magical shield and she won't use it no matter what. Then earlier I was being all sneaky with my archer elven friend and got full, so I decided to dump my magical staves I'd found on him. What happens? He immediately switches from bow to flamethrowing magical staff and burns down the forest!
Thanks. I do remember trying to talk to Lydia, but not getting a line that would let me trade with her. And now, sadly, she got killed. If you give your companion healing potions, will they use them?