I'll go with my new favorite, a K31 Schmit-Rubin. Gun cheap, very cheap. Silly accurate too. Somebody makes a scope mount that replaces the rear sight, slap that on along with a Leupold Intermediate Eye Relief (IER) scope and you have instant scout rifle. For that matter the irons are quite adequate. Personally I am going to make a mount for a Zeiss ZF-4 I have, I got it cheap, a glass of comparable quality ought to be 500 bucks.
Ammo, not the cheapest, but at 180 bucks for 480rds online it's not bad. Compare this price to .308 match ammo price because that's what this stuff is in quality. I got 60 rounds last night at the local gun merchant for 30 bucks, whereas a 20 box of Federal Gold Medal Match .308 costs 18 or better. Bolt guns should not be a quantity issue where you buy the cheapest crap surplus.
For 500 bucks you should be able to field a scoped rifle and 480 rounds. That rifle will hit anything you can.
I had a very nice Rem 700 with Douglas bbl. , trick trigger etc. I sold it for two reasons, I was too cheap to buy the good scope it deserved rather than the crappy one it came with, and I did not have the time to put into bolt-gunning since a lot of driving was going to ensue for ranges over 200yds. Best 100yd group was 5 shots from a bipod into .54" so the baby shot. I will get another built as soon as I shell out the pesos for a left handed action, right now the K31 and M-1A satisfy my accuracy urges without sinking 1500+ bucks into a bolt gun project.
As for scopes, I say get a rifle with good irons first. Unless you know how to shoot them well before buying glass scopes are just a crutch and I feel hinder understanding of your gun.