300-350 would be my limit with a 30-06. I think you could do ok with 168gr heads or 180gr. Although nothing fancy, I had a handload using 180gr cor-lokt heads and H4895. Worked great in a 700 remington. Deer have fell to it several times with ease, been doing the NH moose lottery with no luck yet.
Definitely can find a good deer and elk bullet with little to no problems.
What gun are you using? IF the gun is lightweight, I'd lean towards a 165-168 bullet. 400 isn't that bad with a 30-06, a good rest, and a rangefinder. 400 anything takes practice. IF price limit your practice, I would opt for less expensive bullets than skimp on practice. A cowoker goes elk hunting almost every year, he uses a 308 browning with 165 sierra game kings with no problems. Only issue he has, he doesn't get a long shot, it's often a 75-100 yard shot in the woods. Go where the game is I guess. He goes somewhere near pegosa springs colorado.