Pretty much, it goes from best to cheapest:
The main thing to look for is the derailleur hanger, most likely it is built into the frame, but some cheap ones have a claw type hanger on the derailleur itself. If your frame has something like this
you have plenty of options. If the top of the derailleur looks like this
, you need a claw mount type derailleur. I'd probably go with Altus in the first case, and you are probably stuck with Tourney in the second case. Both will work fine, and the price between the two is generally small enough to go with the better one.