Re: .22 Rifle Suggestions
As a bow hunter I can tell you that a broadhead through the chest cavity of a animal is fast and humane and Quiet. I would check the local laws about firearms in town you don't want the coppers snooping around for a stupid coyote.
As for 10/22 it is a sweet little 22 and you can get a good used one at your local pawn shop for about $150 or less.
For varmints in town i would also recommend the arrow, cross bow or standard bow you should easily make a 30 yd shot with practice.
"What we obtain too cheap, we esteem too lightly: it is dearness only that gives every thing its value." Thomas Paine