Ahhhh, the 3006 vs 308 debate carries on through the yet another winter thread...
Before I comment on the time honored debate
I'll respond to the op.
IBD, some things to consider, first off Bambi or Bullwinkle will not care whether you shoot a 3006 or 308 so just forget about that for now. It's all about shot placement, which in effect is accuracy.
While you can have carry hunting rifles you can paper punch with and target rifles that you can hunt with
the more you compromise toward one use or the other, the less suitable it will be for the original use.
Think about the overall weight of the rifle. Most folks will want to keep the all in weight of a carry rig hunting rifle under 9lbs. That includes a full magazine, scope, and sling. This varmint rig is at 10 lbs before you start. Unless you are planning on truck and stand hunting only I would suggest something a little trimmer. While I do truck hunt more than half of my hunting is on foot and a big chunk of that is in mountains - 10+ pound rifles get old fast when you carry them all day. My two goto carry rigs are about 7.5 and 8.5pounds.
Barrel length, while I prefer a longer barrel because for me they seem to "point" better than a 18" to 22" barrel, IIRC the velocity gain or loss per inch of barrel with this type of cartridge is in the neighborhood of 20-25fps per inch - not enough to be a material consideration. For a hunting rig I would council you toward a 22" - 24" barrel.
Detachable vs fixed magazine, while I like the concept of a detachable magazine in my experience, for hunting, it makes no difference in readiness and is just one more thing to lose.
For the kind of money you are spending I would suggest looking at an all weather Ruger Hawkeye, a Winchester Model 70 extreme weather (stainless steel and synthetic stock), or the equivalent SS & synthetic stock in a 700. I have shot all of these with outstanding results. While I don't care for Remington's they do shoot. One of my hunting partners out of the box extreme weather Model 70, in 3006, shot sub MOA for me when we were setting it up three years ago.
Just my opinion but I would try to spend as much on your glass as you do on the rifle. And please consider a 3-9x40 with good glass over a lower quality junior Hubble telescope. You don't need more than 9 power for 500 yard shooting and it will mount in a way that facilitates a better cheek weld than a 50 or 56mm objective bell. Buy good quality mounts, think Badger, Nightforce, Talley, or Warne. And invest in a baby torque wrench so you do not over tighten them. A suggestion? Zeiss 3-9x40 Conquest with the 600 yard ballistic reticle and Warne rings. It won't break the bank, it will give reasonably good performance, and it will provide hold over points past 350 yards.
Distance shooting is harder than it sounds and requires a ton of practice and good glass. I just shoot to 500 yards and it has taken a while to get very consistent at those ranges. I would focus on getting very consistent shot placement out to 500 yards before I pondered long distance shooting. As well, by the time you get good to 500 yards you will have a lot better idea of what will really work at long distance.
Now the 3006 vs the 308...
It doesn't matter.
BUT
the 308, in my view, is NOT inherently more accurate, it recoils less, so most folks tend to shoot it better just my opinion.
Here is a link to guy named who did the best test I have ever come across.
http://riflemansjournal.blogspot.com.es/2011/04/cartridges-sibling-rivalry-308-vs-30-06.html
This guy, German Salazar, basically found that the 308 wins more because it is easier to shoot, because it recoils less. All other things being equal there is no difference in accuracy between the two cartridges. His inquiry, with all due respect to the posters on this thread, was very objective and is worth a read.
At the end of the day I still like the 3006 better than it's smaller, weaker cousin, the 308.