If you don’t mind a bolt-action rifle, Savage makes a very accurate .308 that goes for about $300.
My “plan”, since I am new to this, was handgun first (did that in August), then, Ruger 10/22 for Christmas (done), then shotgun (used 1100 at auction last week), ARs and bolt actions to follow the next 2-3 years. I am looking at bolt actions now and am leaning towards Thompson Center Dimension that I can swap between .223 and .308. I got to hold one at a gun auction last week and it felt good. That way I can be working with only 4 calibers plus 12 gauge, .40, .22LR, .223/5.56, and .308/7.62, across 7 “guns” ( XDm, 10/22, AR and bolt actions in 5.56 and .308, and 12 gauge).