Checking a barrel for straightness is half the battle. It is the internal consistency that is hard to check unless you have an air guage. Ultimately, holes in paper will tell the tale.
As has been suggested many times, a Savage HB in a 223 with a 9 or 7 twist will do all you want AND let you practise without breaking the bank or eating up too many barrels. With proper bedding and good load tuning, there is little doubt that you can have a 1/2 to 3/4 min rifle at 200yds and a sub MOA rifle at 1000m IF you learn how to dope the winds.
75gr Amax or Berger, Varget or similar, CCI 450 or BR2, Win cases but Fed, Rem, Lapua, LC will do too. Just keep them from the same lot and do some basic prep to ensure consistency. Use dies that allow you to load ammo without runout and an accurate scale that will be consistent to the same tenth. These things don't cost much money but are critical to good LR success.
In time and as your experience grows, you can explore all the wonderful cartridges which are only a barrel swap away. These will all cost more to shoot and many will have much lower barrel life but the reduction of wind drift at LR will improve.
First thing is to learn how to shoot at 200yds. If you get a load dialed in and you can dope well enough to shoot 1 to 2" groups at 200yds, shooting out to a mile is only about adjusting your scope.
The basic learning skills that are necessary to shoot tight groups at short range are the same for shooting far.
If you get to where you have a fair number of 1" groups at 200yds, hitting at LR will happen very quickly cause you already know how to get it done. You just need to range, dial up your scope and hold into the wind.
Yes, it's that easy.
Jerry