What's better- a mattress pad or a featherbed?

I’m getting ready to head off to college and I have a bad back, so I’m looking for something that will improve the comfort of my mattress. Unfortunately, I’m totally clueless as to what I should buy.

First off, I don’t really understand the different benefits of a mattress pad vs. a featherbed, so any opinions in that area would be greatly appreciated!

Secondly, I’m not sure what material would be best for me. Here’s a little background information:
-I have bad allergies, so if I go the featherbed route, down is out. It would have to be down alternative or a “fiberbed.”
-Memory foam isn’t my favorite, but I read that it’s great for bad backs, so I am (reluctantly) open to it if there isn’t a better option.
-I’m very particular about the temperature of my bed, so something that wouldn’t make my bed feel warmer would be ideal.

If any jellies out there have a favorite mattress pad/featherbed out there that they can suggest, feel free to link me to it! I don’t have an unlimited budget, but I’m willing to spend up to $80 or so on a good, quality mattress pad or featherbed since my back is such an issue. Thanks for any help!