"...Does the .223 even go 500 yards?..." Of course. It just drops a great deal depending on the bullet used. Remington factory ammo with a 55 grain bullet drops 58.6" at 500 with a 200 yard zero. And has under 200 ft-lbs of energy left at 500. A 69 grain bullet drops 45.4" at 500 with the same zero. It has far more energy though. 473 ft-lbs. at 500 yards.
At 300, a 55 grain bullet gives the same energy as the 69 grain bullet does at 500. And drops 8.2" at 300 with a 200 yard zero.
No scope is going to help any of that. The rifling twist matters. As does the weight of the barrel. You need heavy bullets for long range shooting. If your rifle's rifling twist won't stabilize heavy bullets, you won't be accurate enough at 500 yards with a .223.
That being said, there is no one best scope for any rifle or cartridge. A scope only allows you to see the target better. It won't make a rifle that doesn't shoot well, shoot any better. However, any good scope will do nicely, but don't expect a scope to allow you to shoot a .223 at anything but targets at 500 yards.