The biggest problem I have with Remington 'Mountian Rifles' is they have CRAP plastic stocks that do WEIRD STUFF...
They are just TOO flimsy.
Rem 700 has EASY trigger adjustments,
And everyone makes stuff for them if you don't like this or that...
The Winchester model 70's have a MUCH better synthetic stock on them (Light Weight 'Mountian Rifle' versions) but the action/trigger needs a little work.
The RUGER "ALL WEATHER" is a great buy and makes for as good of Mountian Hunting Rifle as you will ever hope to find.
Not real pricey, easy to work on, accurate out of the box, and you can't beat Ruger for reliability.
I have a Ruger 'All Weather' I've packed for several years, and it's NEVER let me down.
Savage makes some really fine hunting rifles now, but I'm not real familiar with the product line, specifically the thin barrel, light weight versions.
Savage is also a snap to change barrels in.
You will find lots of 'Professional Hunters' and Guides carrying Savage since you can change barrels in a SNAP, and don't have to lug around 4 different rifles for one hunt.
As long as you choose bolt face sizes that are the same for your different rounds, the barrel literally takes less than 2 minutes to change!
(last trip to Alaska, I hunted antlers, bear and wolf on the same trip, so I took two rifles.)
Since this is your FIRST rifle,
1.I would suggest something made in the US,
And I would suggest something COMMON,
So if you don't like it, out grow it, decide to hunt something different, it wasn't super expensive to buy, and not super hard to sell if you want something different.
US made means there will be spare parts for ages to come, and everyone will support your rifle with aftermakret goodies.
2. Stick with FACTORY CALIBERS,
Don't dive off into the strange or hard to find or handloads only calibers....
Stay above a .25 caliber bullet,
But stay out of the 'Magnum' calibers.
The word 'Magnum' means "Clean out your wallet just to increase the recoil and likely hood of missing your game"
People have been doing just fine with 7mm-08, .270, .308, .30-06 ect. for years, and there is no sense in trying to fix what isn't broke with your first hunting rifle!
Between .25 & .30 caliber will just flat knock down virtually anything this side of grizzly and moose without problems...
No sense creating problems for yourself.
3. Find a local gun shop with STOOLS or chairs sitting around, and hang out a while...
Find the guys that actually HUNT (Somewhere besides 'Hunting' spots on the internet to post up crap) and find out what they use.
Personally, I have two Tikka rifles, but I don't hunt with them, too expensive and nice to beat up.
I look for some synthetic stock that doesn't matter how bad I scratch it up while it's riding in the truck or getting dragged across rocks, banged on trees, used to hold back sticker bushes,
Stainless action that's easy cleaning and I can paint camo or black,
Barrel with good, clean edges on the rifling and a good, smooth, well burnished bore (or I clean the crap out of it and break-in/burnish the barrel myself),
And I go hunting!
Hunting isn't about who has the best designer name in camo or rifles, it's about putting down the animals cleanly, efficiently and humanely as possible.
Any Pro or guide will tell you, the 'Suit' with the $5,000 rifle is ALWAYS the one that needs the guide to put his animal down,
And the guy with military surplus camo and a beat up, but CLEAN rifle is the guy to put things down with one shot!
4. Take your newly acquired and set up rifle out where you normally hunt and set up some targets...
Get used to the things bullets do 'Up Hill' and 'Down Hill',
Figure out where the wind drafts are going to push things around from the gullies and hills you are shooting past.
NOTING, and I mean NOTHING means anything if you can't anticipate where that round is going to impact!
Shooting up and down hill will effect the effective gravity angle exerted on the bullet, even at two or three hundred yards...
And wind does some strange stuff to trajectories if you use small, light weight bullets...
For whitetail, stay around 150 grains with soft point or ballistic point (Controlled Expansion, you don't want a fragmented bullet)....
150 is a good compromise between knockdown power, penetration and wind bucking weight.
Some guys go with lighter, and it gets blown around and doesn't penetrate,
Some guys go with heavier and the bullet is too slow, so you get a lot of drop, and it OVER penetrates...
(In one side, out the other... If it exits the deer, you wasted bullet energy at the target.)
5. Something that IS NOT discussed enough is factory ammo.
There are some REALLY GOOD factory hunting ammo brands out there that will save you TONS of effort & money reloading or buying 'Specialty' rounds...
Winchester is a AMMUNITION COMPANY,
(Winchester firearms are made out of the country, but the ammo is made right in the USA)
And their 'Supreme' or Premium brand of bullets does a VERY GOOD JOB of being both accurate, and expanding to deliver the energy to the target.
Remington brand of ammo must be an afterthought for them, since it isn't really accurate or updated very often.
Federal Firearms is making some of the most accurate out of the box ammo and reloading components on the mass market side.
I am particularly fond of the 'Match' ammo, and the hunting ammo has done well for me on the occasions I've used it here and there.
Then there are the 'Specialty' makers,
Black Hills, Hornady, ect.
This ammo has a HUGE reputation, but in all actuality, I can't see much difference between it and the 'Premium' ammo that is much cheaper from the major players.
I keep trying a box of it here and a box of it there, but it's just not any really demonstrateable amount more accurate than the Premium or Match stuff from other places.
6. Like I said before, stick with LEUPOLD optics and stick with FIXED POWER optics!
This alone will save you gobs of cash and make for a MUCH more accurate platform in the long run!
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If you REALLY want a challenge, you can pick up a Surplus Mosin-Nagant for about $80, and tinker with it yourself.
If you screw up, it's only $80 out the window if it's not repairable!
Mosin-Nagant is the forerunner to the .30-06 cartridge, so it has plenty of knock down power for whitetails,
They shoot pretty good, and synthetic stocks, optics mounts, ect. are reasonably priced.
IT will be a DIY challenge! But you can actually wind up with a very good hunting rifle out of the deal for dirt cheap!