Dunno what kind of Rem 700 you have.
If you have a Sendero or Sendero SF in 7mm rem mag, you have a formidable rifle capable of being tuned to deliver 1200yd precision. Maybe not in same 4" 10rd grps at 1000yds as a 30lb bench gun, but very decent...
There is also the potential to ream your barrel to 7mm STW for more velocity.
Velocity plus ballistic coefficiency is what delivers the potential for small groups at great distance. Are you a handloader? Need to study-up on ballistics and performance of various cartridges.
If you got a Sendeo, you've got a better than typical factory barrel and an H-S Precision stock to work with. Rem 700s are easy to change barrels. Buy another magnum barrel in ctg you want on Ebay or Gunbroker and have gunsmith install it. Takes about 30min and cost maybe $30.
Load something like the Hornady 162gr A-Max with .625 bc and learn to shoot it. The Sierra match king 175 or a Berger 180 is the ticket for longest yardage. Learn to handload your ammunition and to tune your rifle.
The .338 Lapua is a specialty item. Takes a larger diameter boltface. Brass is 4x as expensive and hard to find. Burns a lot more powder and only really performs with 250 to 300gr bullets. Bullets are 2-3x as expensive as for 7mm match guns.
7mm rem mag is a superbly accurate round and relatively mild compared to larger bore magnums. Handloaded it can do almost anything you could want. Learn to shoot it to its limits and then decide if you need a 7mm STW or 7mm ultra mag, or 7mm Dakota...
If your rifle is a BDL or ADL model 700, it will be capable of decent accuracy for its intended role as a hunting rifle. You can buy a new stock and heavy contour barrel once you get into the sport. A custom barrel is a great improvement to work with.
First thing you can do to be sure your rifle is capable of best performance is to have the trigger tuned to 2.5lbs so you don't have to fight the trigger. Handloading to mild velocities will enable you to get used to the recoil and not develop flinching habit.
Magnums are not really a beginner centerfire rifle, but if committed and if you can tune your own ammunition, you'll be fine.
Lots of 7mm rem mag brass and heavy 7mm bullets out there as the round is not currently favored or touted. That works in your favor. Get into handloading now and learn your rifle, then you are set to understand what improvements you want.