Well, I sight 150-grain .30-06 rounds two inches high at 100 yards and have made several 200 yard shots with point blank aiming. I use 06's for deer and feral pigs so I get on fine with 150-grain rounds. I have some 165 and 180-grain rounds and I don't see an appreciable difference out to 200 yards with any of them. I've got a number of rifles and if I could only have one it would be an 06.
For an inexpensive round, you might consider the 165-grain PRVI Partizan .30-06 cartridge from Serbia. I've had very good luck with them.