There are several magnums on GB with buy it now prices of $700 or less including a 338WM, 300 Weatherby's, WM, 7mm mag, and a surprisingly nice Belgian FN browning in 300WM
Possibly a Savage 212 with some good Sabot rounds.. or for that price you could get into a decent muzzleloader
Another that comes to mind is a Remington 700 SPS in .300 Win Mag, Bass Pro was selling one with a scope already mounted for under $600 I don't know how long the scope would last at that price point though.
Weatherby Vanguard, 300WBY, accurate, solid, easily under $700, and will beat the snot out of you at the bench. More retained energy at 300 yds than 308 at the muzzle.
Contender or encore in 375 Jdj is a fun thumper. A lot of people don't appreciate the variety and ease of changing calibers with the Tc's . Plus you can order almost any caliber for the encore and switch between pistol and rifle barrels easily. Most are right around 700 or lower and barrels run 200-350 for customs.
Both Savage and Howa offer sub $700 rifles in .375 Ruger. If you look around you can sometimes pick up an old Mark X Mauser in .458 Win Mag for around $700.
IIRC, my buddy payed like $400 for his 300RUM. It's a rem700, blind magazine, Tupperware stock, 24" sporter barrel (the contour smaller than the varmint barrels). It has a little kick