I shoot a Mossberg ATR in .30-06 it won't break the bank and is a fine shooter. It's a bolt however unless you want to spent over $1000 for a lever action Browning .30-06 you can hang up that idea. Remington makes a pump, and a semi as well. I would go pump it's not actually much slower than a semi, and much more reliable, and durable.
The .30-06 is an old tried and true caliber. There isn't 10 cents worth of difference between it and a 300wsm, or a rem 7mm mag. 3" drop difference at 500 yards, and 500 ft lbs worth of energy (all delivering well over 1000lb of force) all travelling between 1900-2200 fps. And those aren't hot loads or even Hornady loads. That's just standard loads.
Basically at 500 yards any of the 3 are hitting about like a .30-30 at 100 yards. I've seen elk taken at 300 with a .243 so really too much beyond that is excessive. However most people can handle a .30-06 recoil fairly well. Many cannot handle the Rem 7mag, or the .300wsm that well. I've got a buddy with a rem 7mag he can't stand to shoot it more than twice at the range. It just varies from person to person.