Skeets, how old are you? With 13 at the end of your name it makes me think your 13 or something like that. Well, if you are, then theirs no way your gonna have the money to spend on ammo to shoot the 17 HMR
Take a look at how close to were your gonna be hunting and look at were that bullet is gonna be flying. Were is it gonna hit when its all burned out?

And a list of good guns that I think would work just fine.

A good Ruger 10/22 with a 4x scope is fun and a good hunting gun. $180 bucks, gun, scope, ammo and a few small toys for it.

Marlin 880 SQ, now that's a 22 lr sniper rifle. $200 bucks or so for the rifle. For about $300 bucks (give or take a few bucks), gun, scope, tripods, sling, ammo.

If you are wanting to do coyote and coons at long range (100-200 yard if you are a good shot) The Marlin 882SSV, About $230 for the gun. Put a little over $300 bucks down and you can get another really good sniper rifle. Gun, scope, sling, tripods ammo. I get 1/2 inch groups with mine with cheap ammo at 100 yards.

If you really want to spend some money for coyotes get the Marlin's .17 Hornady Rimfire Magnum bolt action rifle, for $300 bucks an SS gun and a scope. For about $380 you can get the gun, scope, tripods, sling and some ammo.

If you wanna have some fun. Get a Ruger Mini-14 and for about $400 bucks you can get a NIB all weather model 223, add another 100 bucks for a good/cheap sniper scope, another $20 per mag for 20 round mags, $10 bucks for a sling, $50 bucks for a 1000+rounds of 223 and go out and have fun! My Mini-14 shoots really well at 100-300 yards!

With the guns I just listed, you gotta think on were that bullets gonna hit.
If I was you and knew that I could discharge a firearm with out getting the cops called on me I would use a good 12 GA

$220 you can get a Mossberg 500 all weather model 12 GA shotgun and for 10-15 bucks you can pick up a choke tube.

For about the same price you can get a Remington 870 with a wood stock.

For like $300 bucks you can get a very good Winchester 1300 12 GA pump shotgun with the all weather model stock.
Or if you wanna keep it simple and use the good old single shot shotgun, New England shotgun with the 12, 20 GA barrel or the 410 bore barrel.
I use a New England single shot 410 for rabbits and grouse using 3 inch mag #4 shot but if its all really close range, I'll go up to the #6 shot. Only 3 inch mag for me though.

For 12 GA, shoot #4 buck for coyotes and maybe even coons. I use 6 to 8 shot for rabbits, grouse and other small game.

If that does not work, a good old ten pump BB/pellet gun works just fine. Stay away from CO2.
Them gamo single shots are really nice to.

Hope this helps