Firstly, you should be looking at 10-12 footpounds- (not fps, as this is not an indication of power). What budget specifically are you looking for?

I was looking at between $100 to $150 tops. All the guns in Cabellas catalog are .177. I know you will get more momentum or knock down power with .22. So the .22 can have a lower fps than the .177. The .177 has a flater trajectory. I know the weight of the pellet plays a part too. What can you recommend? Thanks.

on cabellas, a good option would be the beeman gh950 in .22. I run .22, and personally i think they are better for hunting. There is a saying which goes '.22 for fur, .177 for feather'-but this isn't really true at all. your main concern should be the weight of the pellet- heavier is better, but you have to be closer! everything is a question of balance

if your not going to spend loads on a gun then i would recomend the smk super grade xs20. it cost only £140 but it comes with a silencer, which is nessercery when hunting rabbits. but if thats too exspensive the you should try your nearest gun dealer
and speak to them about getting a second hand rifle.
and explain what it is you intend to do.

What is your main interest. outdoor pursuits