Well, the general answer to your question is this:
We live in the golden age of turnbolt rifles - there are a veritable plethora of quality, affordable turnbolts, so that's the good news - your choices are many, and the value factor extremely high. The bad news is that your choices are many, making it tough to decide. Sticking with a turnbolt is a very good call, IMO. Current production includes:
1. Remington 700, in its many many varieties (submodels)
2. Remington Model Seven
3. Remington Spartan (Zastava) 798
4. Winchester 70 in several varieties
5. Browning A-bolt & X-bolt in many varieties
6. Tikka (Beretta) T3
7. Sako (Beretta) 75 & 85
8. Steyr Pro-Hunter & other models
9. Weatherby Mark V
10. Weatherby Vanguard
11. Howa 1500 (same as Weatherby Vanguard)
12. T/C Icon
13. Savage 10, 11, 12, 14, 110, 111, 112, 114, in its many varieties
14. S&W I-Bolt
15. Izhmash bolt rifles (Sobol, etc.)
16. FN Herstal (.308 only, I believe)
17. Marlin XL-7
18. Mossberg 4x4 & ATR
19. CZ 550
20. Remington 710 / 715 / 770 / Whitetail Hunter
21. Kimber 84
22. Custom & semi-custom jobs like Cooper & Others....
In the "Less than $600 category", if buying new, not used, you're best off, IMO, looking at a CZ 550, Tikka T3, Howa 1500, Weatherby Vanguard, Remington 700 SPS, or one of the Savage models. PM me for details on why. Maybe a Zastava/Spartan 798, but it wouldn't be my first choice. CZ 550 may come in *just* under that price, or just a tad over that price, but it's probably the best rifle in this general category. Neither it nor the Tikka T3 would make the "under $550" category as the others would. Nor would high-end Vanguards.
If buying USED in the under $600 category, then I'd look at a Browning A-bolt, Remington 700 BDL or CDL, Remington Seven, or T/C Icon as my first choices (note: this does not include the Rem 710/715/770). Better yet, if you can find a Sako or Steyr in your price range, that'd be the way to go. There are probably precious few T/C Icons available used at this point, but if you can find one, it's a heck of a rifle, with the 60 deg bolt throw, like the Browning A-Bolt.