Best Hunter rifle

[tom96]

i would go for a .20 cal beeman r9 and a really ice scope, rings, pellets and a v-mach tune kit, as well as a sling.
  dont worry bout coons with it, if the shot is good, it will be DRT. ive shot one at 25-30 yards with my tuned 34, and it was done with 1 shot, on the hunting gate you can see shadow post coons taken with the chinese clone of the r9.

[Jaymo]

The R9 in .177 kills squirrels as dead as they can get. I've had more one-shot-stops on squirrels with my EAA badged, HW85(long barreled R9) then I've ever had with .22 LR solids.
I have as many .22 air guns as I do .177. I like the .22 air guns a lot, but my .177 HW is a squirrel hammer. That's not to say that my .22 air guns aren't. My .22 B30 (Chinese Diana 48 clone) is very deadly on squirrels.

[Bullit]

Well, I'll third the vote for the Diana 48 in .22 cal.  for the rougher field use and power.  You could be set up with a deadly accurate shooter, a very good 3-9x Leapers UTG scope and mount...all for LESS than your $600.00 budget.  I'm a user/fan of the M48/52, and they're proven.
Edit:  I know you said you wanted .22, but I thought you also might consider getting a .177 as well.  There are fine .177 high power, fixed barrels that you could pick up.
I use .177 heavies (JSB), and have no problems with quarry up thru coons.  They are Very flat shooting and quite effective at 50 yards.   But if the Bandits are "Bigguns", temper your range, (I tend to be comfortable and confident at 25-30 yards max), make sure the fusebox gets a good disconnect signal   Best of Luck to You.