I don't keep up with current prices for them but a plain old standard Springfield Armory M1A should be available for less than the upper end of your budget. I have an older Springfield Armory M1A. No "loaded" options. No "match" options. No frills at all. With issue sights it's a solid 1 1/2-inch group shooter for 5 shots off the bench rest at 100 yards, occasionally straying down to 1 1/4 inches if I'm in a good shooting humor. It's given dependable performance for high-power competition and extended long range plinking sessions.
I'm way out of style but don't much care for the short-barreled versions, preferring the longer barrel to keep the muzzle blast down and farther away from me, along with the ballistic advantage the longer barrel does afford.
Don't be afraid of a good used M1A as may be found on GunBroker or other auction sites. I'd stay away from any that are described as customized, modified, or tricked out. A stock rifle would be preferred to one that's been monkeyed with to conform to someone else's wishes.