You can't beat CZ or the Rem798 lineup for bang/buck ratio for a new "safari" rifle. Maybe a Ruger in 375 Ruger, but I'm not sold on such a new cartridge.
That being said, a 338 Win mag is more than enough gun for everything you can legally shoot with it.
But if you decide to go the custom route, that's pretty economical too. My 9.3x62 build was very reasonable and my smith did great work.