With the budget the OP listed, he can have almost matching Ruger M77 Hawkeyes in BOTH .270 Win, and 30-06 along with a pair of excellent Leupold scopes.
https://www.cdnnsports.com/firearms.html#category_2=FIREARMS/HUNTING RIFLES&manufacturer=RUGER®&pg=2
As long as he doesn't mind Hogue rubber stocks. Myself, I opted for the one in .270 Win and a regular synthetic stock version in .308 Win.
IF you live in Alaska, and don't mind recoil, the .300 Win Mag is probably the best choice, followed by the 30-06. Anywhere else, the .308 Win or .270 Win makes the most sense, to me at least. The .270 is a milder kicking flatter shooting version of the .30-06 and loaded with a 150 gr Nosler Partition, or similar bullet, can certainly do the job on any deer and capably handle elk or moose with proper shot placement. (Closer is better for all hunting and humane taking of game.) The .308 Win is right on the heels of the 30-06 but does give up some performance with the heavy bullets. I believe it does have an accuracy edge over the 30-06, at least it has demonstrated that in my experience.
As for the lack of bullet variety for the .270, that is a lousy argument offered by 30-06 fanboys. How many different types of bullets and weights do you need? Will your 30-06 shoot ALL of them equally well? Of course not. You will ultimately select 3 or 4 at most that meet your hunting or target shooting requirements and use those. For heavens sake, if you tried to find an optimum load for every .308 bullet available for your 30-06, you would wear out your original barrel and have to start all over again with your new barrel.
I haven't started on developing a hunting load for my .308 Win., but have settled on a 130 gr Nosler Ballistic Tip for the .270 Win. for deer. I have developed my target load for the .308 Win using the 168 gr Nosler HPBT and IMR-4064. I will try that load with the same weight Ballistic Tip in my new Hawkeye and see how it goes.
Let us know how it goes, Toystry. Please consider what you are planning to hunt. If it is mostly deer/antelope with a possibility of elk/moose someday, maybe, consider the .270 Win or .308 Win. Abundant inexpensive factory ammo available, milder recoil and more than adequate performance for 95% of hunting demands.