I would get one of the 700 Dick's specials. They put them on sale for about 400 bucks after rebates.
I thought the same thing a couple of Christmases ago. Bought one in .308 with the varmint barrel for under $400 after rebates to use as a cheap long-range rifle.
The stock flexed too much to use a bipod. Add $200.
The trigger was lawyered-up to be unbelieveably bad. Changed to a Jewell. Add $200.
The included scope was marginal for 100 yards, useless for 200+. Add $400.
Now it shoots like a $1200 rifle. And it's HEAVY.
I own 4 .22-250s. Ruger 77V, Ruger 77VT Mk II, Tikka T-3 Lite in stainless, and a custom Remington 700. The Rugers are great bench guns, the Tikka is a great walking gun, and the Remington is the most accurate (for roughly the combined cost of the other three).
I have taken hundreds of ground squirrels with the two Rugers, many in excess of 300 yards. I bought the Tikka for a walkaround coyote gun, and if I were doing it over would have gotten it in .223. I've since displaced it with a CZ in .223 - fantastic little gun. The Tikka will reach out there with the rest of the -250s, but if shooting from a bench it's nicer with the heavier guns. The Remington was built by my father-in-law, and has a very, very light trigger. Truly a bench gun, but it will shoot 5 shots in a ragged hole at 100 yards if I do my part.
When I started shooting varmint, I picked up a used Mark X sporter with a Western Field 6x fixed scope for $125. The previous owner couldn't get it to group. I opened up the barrel channel and bedded the action, and it went from 2.5 MOA to under 1 MOA with Federal 55gr factory ammo. I learned more about ranging and trajectory with that rifle than any other - and shot a lot of squirrels with it. Lost it in a burglary.
If I had it to do over, I'd go .223. At 300 yards, the .223 kills 'em just as dead with longer barrel life and less noise. I haven't shot a varmint with a .22-250 since I got my CZ in .223.
