Honestly, for shooting small game at anywhere from 50-600 yards, I would buy a rangefinder as well. Some scopes have bullet hold over marks for different ranges, but they are generic marks that may or may not match your results from your rifle. If you are trying to hit the vitals of a deer at 300 yards they may work fine. If you are shooting at squirrels at 600 yards its something else. Even the moderately heavy .223 bullets are dropping around 5 inches per 10 yards around 600 yards. If you think the little guy is at 580 yards when he is at 600, you are going to be off by a good 10 inches if not more(lighter bullets). So shooting at unknown distances on small game, even with a good mildot reticle which allows you to estimate range, is going to probably be to imprecise to make hits, at least first round hits.
I think you are expecting a little much. Honestly, if you don't know if you will need a range finder to hunt at 600 yards with a .223, I doubt you should be shooting at living targets at half that range. Nothing personal, but it is one of those things where by the time you have the skill to shoot out to 600 yards at 6" targets, you know what you need to do so. For paper punching/plinking out to 600 yards, sure you don't need a range finder. Be prepared to miss on the first shot quite a bit, but you have plenty of extras to walk onto target.
As for what scope. I would say something with a maximum magnification in the 15-25x range. At 600 yards, a squirrel/fox/coyote at 15x magnification is going to look like he is at 2.5x at 100 yards. That is pretty small still. At 20x and 600 yards he would show up like he would at 100 yards with a 3.3x scope. At 25x and 600 yards he would show up about like he would at 100 yards with a 4x scope. All of these are still fairly small but doable.
Pick a scope as close to your max budget possible and you should get about as much glass as you can.