Savage gets my vote.I have a couple and the accu-trigger is sweet! IDK if they used to be just so-so and got a tarnished rep or what but all i have and have shot have been excellent.
Here are two that will shoot with any Savage or otherwise.
Both purchased under $1000 each
Two Tikka M595 Continental Varminters. 22-250 in front, .223 in back.
Unfortunately they are no longer made. The T3 is there replacement. The T3's are not the same gun as these old girls but still a excellent varmint rifle in there own right and worthy of being considered for any varmint hunter. You can find them new under $1000 and used with a heavy barrel for around the $700 range. I strongly agree with the other Tikka post! +1 for the Tikka!