In Fallout: New Vegas, I've gotten the companion with the pneumatic glove, but she won't put on the body armor I give her.
What are the restrictions for weapons and armor with companions?
How can you tell what a companion will wear or use?
Companions will generally not wear faction armor. They will equip the armor with the highest damage threshold, although I recall that there are some edge cases where that won't work. For weapons they will use the weapon with the highest DPS available, you should take the companion's skills into account. Don't forget to give them the right ammunition for the weapons, only their default weapons don't use ammo.
Veronica will also equip Brotherhood of Steel armor, even though that is faction armor.
I don't think there is a better way to see what they accept than just giving it to them and try it out.