As you stated in a post you will be shooting to a max of 300 yards. The 30-06 is very capable of making 300 yard shots. If you would like more power and a flatter trajectory look for some Federal Premium High Energy or Hornady Light Magnum loads. These loads will propel 150 gr. bullets at 3100 fps and 165 gr. loads at 3000. This gain in velocity will flatten your trajectory and increase your downrange energy levels. Going to a 7MM or 300 Magnum will not make your bullets death rays. Proper shot placement will still be required to take a game animal. Invest the money you would spend on a new gun in ammo for practicing and upgrade your scope if you are not using top of the line glass.

If you just have to have a new rifle I would look to the 270, 7MM, or 300 WSM. The 7MM Remington Mag. & 300 Win. Mag. are also viable choices. The recoil from these will not be severely worse than the 30-06 you already own. If you go to the 300 Rem Ultra Mag or 30-378 you will experience noticeably more recoil and muzzle blast. Still with any larger cartridge that you buy shot placement is critical. Shooting a deer in the hoof with an ultra mag won't kill it any better than shooting it with a .22. This is my .02 cents worth.