Sniperboy, if I were you, I would seriously look at the 243 for your varminting needs. A 243, with an 8, 8.5, 9, or 10 twist barrel, you can shoot the VLD type bullets or the deadly 87grn V-max. The 243, with a 26" barrel, will push the 87grn V-Max at around 3350fps or faster.
I would also look at the Cooper too. However, if money is an issue, look at the Savage 12BVSS or the Remington VLS. The 22-250 is a great varmint caliber, however, IMO the 6mm's are the best long range caliber for varminting. With the 6mm's you get the following; low recoil, bullets choice, range advantage over the .22cals, and more energy on target.
I personally shoot the 6x284, however, it's a bit of a barrel burner, but I love it for long range varminting.