its hard to beat .223 as a 'general purpose' varmint/predator caliber. light recoil, wide availability of ammo and it can be cheaper to shoot than most centerfire calibers.
for $560 you can get a Remington SPS Varmint in .223, .22-250, .204 Ruger or .243 at SIR mailorder.
heres a review: snipercentral.com/remspsv.htm
its pretty much a 700 Police at half the price, without the HS Precision fibreglass stock and matte-blued instead of Parkerized. you could order a laminate thumbhole stock from someplace like Boyd's or Richards Microfit down the road and its a simple drop-in. tonnes of aftermarket accessories for the Remington 700s, its the most common rifle action.
consider this though: unless you are taking several shots per minute, where heating up your barrel comes into play, you really dont need a heavy barreled gun - first shot accuracy will be just as good with a lighter barrel. laminate also adds a retarded amount of weight.
i have a .223 700P and scoped with a heavy varmint scope, bipod, etc its over 14lbs. it is not pleasant to carry around while trekking across fields all day.
if you find you dont need a heavy barrel you could simply order a Stevens 200 in .223 or .22-250 for $300, theyre a very accurate 'no frills' entry level bolt action, search the forum for hundreds of threads on them. you could order your laminate stock for it right now, and be out the door with a thumbhole laminate varmint gun in the caliber of your choice at $500-600.