If you are looking for inexpensive, I would suggest a NEF handi rifle. I own 2 of them(.223 and 22 hornet) Yes, it is a single shot, but they are shooters, and don't cost a lot of money.

I don't personally have any expirience with the 17 rem, but it does have a faithfull following of varmint hunters, however i don't think the handi is offered in this caliber right now.

my 22 hornet shoots pretty good with winchester 45gr. soft points( alot better than Hornady 35gr. v-max) and open sights.

I don't reload and have found the hornet to be easier to find while the 17 is a bit scarce.