The Vortex scopes are going to be a bit over $400, especially the PST line. However, if you can make it work then go with those.
If you are dying to stay under $400, then I currently use a Millett TRS-1 on my Remington 700. It works great, and its adjustments are accurate, tactile, and consistent. It does not have a zero stop (which would be nice), and the reticle is in the second focal plane. Those are the two main complaints I have with the scope.
For $300, it isn't bad.
The biggest thing regarding caliber is, do you reload?
If you don't reload, then you should pick a caliber that has factory produced match ammo if you are wanting to shoot out to 500 yards. That pretty much leaves .223 and .308 (which isn't on your list). If you do reload, then I would go with .243 or one of the 6.5s.