I have been going through this exercise since Dec 2008.

7mm-08 with 140-gr bullets is the starting point.
.308 with 150-gr or 165 is good.
Short action and barrel cuts off a little weight. Handier.

If you go 22-inch barrel, a .30-06 with 165-gr is much better.
.270 Winchester with 130-gr or 140-gr BT is the flattest shooting.
.280 Remington or 7x64mm with 154 or 160-gr is ideal for me: flat shooting and the energy of a .30-06 at 300 yards.

The drawback of the 7mm-08 and the .308 is the real-world muzzle velocities from a 22-inch or 20-inch barrel often being 150 fps less than advertised test lab velocity.

1. Tikka T3 SS Lite in 7mm-08, .308, .270 Win, or .30-06. $620.00. 6.0 lbs naked. Drawback: no iron sights.

2. Remington ADL in .270, .280 Rem or .30-06 with 22-inch barrel and iron sights. Change the front blade from bead to sturdy steel post. Buy a nice one used for $400.00. Buy a used wood take-off stock, seal the inside, glass bed it, and let it get beat up. Save the nice stock. If you want moisture protection, Gunkote it yourself. 1.25-inch groups all day long are plenty good.

3. Remington SPS Camo for $475.00 new in .308, .270 or .30-06 with a 24-inch barrel. If it is too long, cut it back to 22 inches and recrown. If you want moisture protection, Gunkote it yourself.

Mount a Picatinny rail on rifles 1,2 or 3.

Add a second forend swivel stud in case you rip one out climbing.

4. Marlin XSC in .308 or XLC camo in .270 or .30-06 for $300, half the price of the T3. Comes with a Weaver rail.

SCOPES

Shots are going to be under 300 yards, so the setup for any of these is a max 3 inch rise and fall below sight plane out to 250 yards, and maybe 7 inches low at 300. All you need is a 4x or 6x scope. You aren't going to be shooting at dusk like from a deer stand 200 yards from your truck. Forget all the light-gathering blather and ballistic reticles. Weaver K4 or K6. Mount it in Warne QD rings. If you really want a variable, get a Pentax Gameseeker 3-9x40, Swift, or an EA Brown 4-12x40AO. At least take a second cheap scope in the same rings as a spare. Use the money you saved to buy a rangefinder if you aren't good at judging range. Bushnell will do. You aren't ranging 600 or 800 yard shots.

What did I buy? Tikka T3 Lite SS in .30-06 NIB for $450.00.
Then, last month I ran across a used Steyr SBS Pro Hunter stainless camo in .308 with a Swarowski 3-9x46 AV for $500.00. I am swapping out the Leupold bases and rings for Picatinny and Warne, and adding iron sights next.