I am not shooting at animals beyond 250. I want a rifle with a large enough caliber to shoot Moose and Elk at reasonable distances but I also want to use it for long distance targets. Two different purposes with one rifle. I don’t have money to buy a rifle for every purpose. Thanks.
You may consider a .408 cheytac for long range target shooting.
If you plan on shooting a lot, get into reloading which will greatly reduce your costs.
I'm glad you made this second comment. I was about to go postal on several of the FReepers on here who can't seem to read. You made it perfectly clear in your post you were wanting to target shoot out to 600 yards but were going to hunt at normal ranges. Why else would you ask for a rifle that could do both?
I think reading comprehension classes would help many of our FReepers.
My advice is coming from over 2 decades of bench rest and freehand silhouette competition, as well as combat sniper/special forces service.
The best choice you could make in regards to the needs you express, would be for you to buy a reasonably good used Remington 700 BDL with a long action. (30-06 or belted magnum)
Take it to a good gunsmith and have the bolt and locking lugs trued and accurized. Have that same gunsmith rebarrel it in either a high grade #5 or #6 Hart or Douglas. Have it chambered to either an 8mm-06, 300 Win Mag, 338 Win Mag, or simply make it a 30-06.
Then have it bedded in a good composite stock and do not cut the barrel any longer than 20 inches and more importantly, have it crowned. It would also be wise to read up on accuracy and shooting technique. Then, take it to the range and practice, practice, practice. Not to mention, learn to custom hand load your ammunition. Do this, and you will have a far better rifle than you could ever buy off of the shelf, and for a third of the cost.
From what you describe, anything larger than a 30-06 is overkill for game in this continent. The 30-06 has more than ample power, and will easily handle any of the largest game on this continent. It is also a stellar long range round and is effective out to 1,000 meters.
For the largest and most dangerous game, like Brown Bear or Yukon Moose, I recommend at least a 338 Win Mag or larger. My personal and favorite choice for these animals is the 375 H&H.
Sounds like 30:06 as Sampleman stated.
Personally, I have found RugerM77 rifles to shoot well and are reasonably priced. I hunt with a M77 Ultralight “Mountain Rifle” because I carry it more than shoot it, but at the distance you say stick with a longer barrel.