Go over to longrangehunting.com they have all kinds of info there and they're not the typical ohrah label whores. 6mmbr.com has some label whores but generally a good group of guys.
I've never shot at 600 but I have been to Quantico on range 4 a a few times shooting f-class @ 800, 900, and 1000. And I've built a few rifles myself. If you want off the shelf cartridges and don't plan on handloading, 308 would work obviously though there are better, like a 260 Remington. My personal preference is either a 6x47 Lapua or its parent the 6.5x47 Lapua.
Custom cartridges are going to get you accuaracy slightly easier simply because they're handloads from the beginning and you're naturally going to do load development and use a projectile with the best BC possible. On the other hand commercially available cartridges are generally cheaper, and by definition more available
You have to decide if you're looking to just shoot, or are you looking to shoot, handload, do development, and have a somewhat touchy rig.
You also have to decide how much you want to be beaten up. You can do 600 with a .223, it isn't going to be as easy with a larger better ballistic co-efficient bullet. But it isn't going to hurt with each trigger pull. You can get all the velocity you want out of a magnum or ultra mag cartrige and get some really good projectiles. You're going to pay the price with every pull on that trigger.