I'm a long time varmint shooter(prairie dogs are my favorite). Since I got my first of many 204's in 2006, I rarely shoot the beloved 220Swift's that collect dust in my safe. With typical varmint loads in factory twist barrels I find the 204R to excell ballistically to 600 yards in all respects but energy, and that difference is not very much. Once you have some brass the 204 is cheap to load for. Try 39gr Sierra bullets first and you might be done experimenting right there.
I just picked up a Savage Model 10 Predator Hunter Max 1. I like it but the price may over shoot your budget. I have only fired 8 rounds out of it but it show potential and I havent loaded for it yet, but there are 39gr Blitzkings waiting on the sidelines right now. This makes my second .204 and I dont think I made a bad choice in the rifle.
A 204 with the new berger 55gr will paste a 22-250 at any range. Im looking at an AR in 20 cal(probly a 20 tactical) as my new coyote rifle. The smaller stuff is great also I just want an 800 yd yote gun.