Some good advice so far. Allow me to expand on that some.
-- 1) Practice, practice, and More Practice! You can not get enough Trigger Time. Pure and Simple sir.
-- 1a) Pick a round that has truly great barrel life.
-- 1b) Also, pick a round that you can get superbly accurate ammo for over the counter. Reloading is even better for accuracy and it is cheaper on you. Trigger Time is King.
-- 1c) Pick a round that will Not Beat You Up while you learn! It needs to recoil enough to make you pay attention to proper form, but not enough to make you flinch.
-- 2) Do not try to cheat your way to the top. Buying a "Laser Beam Of Death" can certainly be entertaining, but it will not Really do you any favors in the long run.
-- 2a) Buy a set of wind flags, and learn to use them. The calibre you choose should be "Good Enough" in the wind but not "Fan-Damn-Super-Tastic". You actually want the bullet to get blown around a little, so you can work on Wind Reading Skills. Wind Reading is probably THE single biggest reason people miss shots beyond about 500 yards or so. Learn it right the first time around, then later you can buy that fancy Laser Beam and you are ahead of the game.
-- 2b) Learn to deal with Mirage.
--- .223 bolt action with at least a 28" barrel with a 1:7 rate of twist set up to shoot the 90 grainers with a powder like Varget, ARComp etc. Even the 90 grainers get blown around in the wind quite a bit, but it definitely will make 1k yards, and the barrel life will be good. Ammo is fairly cheap too.
--- 6.5x47 Lapua bolt action. Fantastic ammo over the counter. Easy to reload for. Good barrel life. Very Very Very good round out to 1k yards no matter how you cut it. More recoil than the .223, but still nice and mild.
--- .260 Remington = You are borderline cheating now.... barrel life will be reasonable, but probably not what most folks deem Fantastic. Lapua is making brass for the 260 these days, so YAAY !!
Damn nice round!
--- .308 Winchester = The Gold Standard by which all others are measured. Some are Platinum, some Silver, some Bronze, but the 308 Win is Gold
That said, either the .260 or the 6.5x47 Lapua will make it look "Sad and Mad" beyond about 700 yards or so. But hey, with the 308 you really will have "Good Enough" on all fronts to learn what you need to, and learn it well. Also, the barrel life is Fantastic.
Ok, sorry for the book, but I was lucky enough to have some one explain this to me when it was time for me to begin learning LR shooting. I thought I would pass it along. Some folks get too caught up too early on ZOMG BOOOOM !!!! Laser beam of Death... and it bites them in the ass hard, sooner rather than later.
Have a good one,
P.S. Buy the absolute best scope you can possibly afford, even it it costs you twice what the rifle did!!! Not all scopes are even remotely the same and a poor scope will kick your ass hard when stretching beyond about 500 yards or so. You do not really NEED a scope higher in power than 24 at most, 14x - 16x if the glass is REALLY GOOD is plenty. Higher than about 18x and you really begin to have to deal with Mirage, also the higher the mag range the worse things like your Heart Beat will distact you ....