Having the hindsight of banging around in the woods chasing moose, caribou, bears and sheep for 40 some years, I have some thoughts on what I'd do starting over. That said, keep in mind, us old gas plants didn't have the choices you have today so we'll go with todays offerings.
From a practical point, I would go with a med contour barrel, synthetic stock and in 30-06. Hunting time is best spent hunting and not worrying about your gun, thus the synthetic stock. The caliber is capable of 110 gr. to 220 gr and does it well so you can adapt to the hunt, i.e.. more practical. With your budget I would look at a Remington 700 SPS on sale at Cabela's for under $600. I would spend a couple hundred having it blueprinted(barrel trued along with bolt face and lugs) and bedded. I would put a Leopold Vx 3i in 6.5-25 for somewhere around $700-$800. And finally, I would put a Timney or Jewel trigger in it.
Not only would this be a nice hunting setup, it would also be at home on the target range for informal shooting with light or cast bullets.
The gun I packed for most of those years was a 7mm Rem Mag. Great gun that served the purpose but it wasn't one I wanted or had time to just shoot. It came out during hunting season and that was about it. Every couple years I'd load up 20 rounds and when those were down to mag full, I'd load up a few more.
These days I'm more inclined to take my 1903 Springfield 30-06. The last moose I shot was with a Remington 1903A/4 sniper rifle so I have choices and if nothing else, I can go hunting at Safeway on the way home...lol.
Good luck in what ever you choose.