Guessing you have private land to shoot on, fantastic!
Longest public range in our parts is the Manatee Gun Club, down in Myakka City. 1,000 yards (there last weekend) is "it"...had plans to extend to one mile but didn't pan out and it's dead in the water.
Nowhere did the mention of handloading come up that I saw above, which is critical to what you're trying to do. Learning to shoot long range involves a lot of rounds sent downrange, and handloads will provide the best accuracy AND the cheapest cost.
That said, I'd recommend a capable 1000 yard rifle first- and there are many in the 6-7mm that'll get your round count and experience up without killing your wallet- or your barrel.
Sure, you can "learn" on a .338 LM- but why burn up a magnum barrel while you learn?
If I were you, and really had a location around here where I could stretch to 1800 yards (is that what's available where you plan to shoot?), I'd pick up a factory Savage (like the 6.5 LRP) or Rem 700 and get experience handloading, doping the wind and hitting what you're aiming at 1000 yards.
Then I'd move up to a .338 LM or bigger wildcat that'll get you to the 1800 you're talking about.