remington model 700 would be a good choice, if your on a low budget look toward savage.
Amen to that. A few years back, I bought a next-to-new (only 30 rounds through it) Savage 110F in .30-06 for less than $200. That's probably the best money I have ever spent on a firearm. The Savage shoots one-hole groups with 150 gr. Norma 'Jaktmatch' ammo (bought on clearance from Midway) - so I know the rifle can shoot way better than I can (as can my Savage 10FP, which I bought later, 'brand-spanking-new,' chambered in .223; even with Federal 'plain-wrap' 50 gr. HP ammo [funny, given the relatively 'fast' twist rate], it shoots better than I can ;>)...
That being said (and though "beggers can't be choosers" - and I'm not complaining about the price ;>), I wish my Savage 110 had been chambered in .308 (I've built several FALs, and it would be nice to stick with a single cartidge). If there's any chance you'll eventually own another rifle chambered in .308 (FAL, M1A, H&K, etc.), you might want to consider a .308 Savage. But (as others have mentioned) if you might like to go with heavy bullets (I've got some 220 gr. RNSP waiting to try in my 110 ;>), you might be best sticking with the .30-06 (plus I think there are more of the .30-06s out there, if you're shopping the used market).
Good luck! As always, your mileage may vary, etc., etc., etc.
(Finally, and FWIW, I've tried the Remington 710 and was definitely NOT impressed. The Savage bolt action looks like a much better design to me... ;>)