The problem with non-standard rounds is I fear that if production slows for ammunition, those rounds will be scarce and high in price. That leaves me with a rifle chambered in something too expensive to shoot, or too hard to find. High velocity rounds such as the 7mm-08, .300WSM, and even .300Win tear a barrel up pretty quickly.
If I had a larger budget (when I'm not in college), then I would certainly consider a .300WSM as my main choice, or even .338 Lap. Mag. if I could swing it. However, right now I'm trying to get the most bang for the buck, and some of those rounds are much more expensive than .308.
But you can load your rounds to whatever velocity you want. I have loads for my .260 that shoot at 2500 fps and I found one today that gave me the tightest group so far and it was at 2897 fps.
Even if barrel life is only 3,000 rounds, paying for premium hunting/match ammo, you're more than likely looking at prices of at least $1-$1.50/round, probably closer to the $1.50-$2.00 mark if your into match ammo. 3,000 rounds is a minimum of $3,000 and up to $6,000 before you shoot out a barrel. How many rounds do you shoot a month/year? Getting a match grade barrel properly put on an action is going to cost you far less than the ammo you will spend to shoot out said barrel.
Again, I'm really not trying to dissuade you from the .308, just your though process of getting a rifle for hunting and long range at your price range. A rifle for long range hunting is not going to be the same rifle that's best suited for carrying around the woods.
What's the terrain like where you hunt? Do you drive, sit in a tree stand, still hunt, spot and stalk, sit somewhere and glass and take long range shots?
If you're mostly stationary and not hauling a rifle around all day, you can probably get away with a rifle built for long range (at least 9-13 lbs, and then put a bipod, scope, sling on it).
I wanted a rifle to do it all and for the style of hunting I do (still hunting, not sitting in a stand or stationary waiting for deer to walk up to me), I wanted something lightweight and got my rifle scoped under 8 lbs with a 20" barrel. The 20" tube just won't give me the 3,000 fps or so with with 140 grain bullets for long range shooting as the 140s give me the best SD/BC to buck the wind, carry the velocity and energy, and penetrate deep into the vitals.
I decided to get a hunting rifle suited for my hunting needs and down the road, I'd build that custom gun that gets into the prices measured with several 4 digit numbers and is suited for match grade accuracy over long range shooting.
If hunting is your primary gig right now, get a hunting rifle and find what shoots best for it. Your point about ammo shortages - even a better reason to get into reloading as soon as you can. .308 brass (.243, .260 Rem, 7mm-08, .338 Federal all use .308 brass as a parent case) should last several loadings. 100 pieces of brass reloaded several times each will put a lot of meat in the freezer.