Savage
Another vote for some type of heavy barrel Savage, and a used Hog is a likely candidate. I bought a used Hog, with rings and the low end Nikon 3-9x, with bases and rings, for $400 about a year ago. Changed the rings and bases, but rifle is a shooter, as is a similar one a pal has.
Getting to 600, and hitting at 600, two different things. You will need some type of sight system that will let you dial up the distance, or minimally some type of hold off aiming points on a reticle, mil-dots or ballistic plex type rig. A typical duplex reticle with standard turrets, will not be practical. You could work up a 600 zero, but your midrange would be excessive. Zero on at midrange, and you might not have a workable aiming point at 600.
Yeah, good shooters can hit at 600 (and those Palma guys go to 1000 or more) with peep as in a service rifle, or I guess the fine notch and blade of a Springfield, but most of us will find that hard to pull off. I'm gonna suggest the Bushnell Elite 10x fixed. They go for about $200, have 90 min of adjustment, and will allow some precision and target ID at that distance.
The Hog Rifle, with medium bull barrel and short tube, and the Accu-Trigger, is a dandy combo.