"Long Range" is considered 1000 yards.
"ELR" (Extended Long Range or Extra Long Range) is 1000+.
Since you asked for "long range target", my answer is going to be different.
I think a smaller cartridge is a grwat choice for 1k. They teach you important skills like reading wind, while allowing you a lot more comfortable shooting at higher volume.
I shoot out to 1400+ a couple times a month (except for about 3 months when temps rarely get below 95°F, even at 5:00am). My rifles for shooting from 350 to 1400 consist of: 22GT, 6CM, 25CM, 6.5SLR, .260AI, and up to a 6.5PRC.
A couple of hunting rifles in 25SST, 6.5PRC/SI, 6.5SS, 7SS sometimes make the trip if an upcpming hunting trip is on the calendar. My 7RM, 28 Nosler, and 300PRC stay in the safe until it is time to get serious for an elk trip.
I usually shoot between 70-130 rounds each trip. No way you are doing that amount of shooting with a .338RUM or bigger cartridge. Even a good braked .300WM/.300PRC type of cartridge would be punishing at that fire rate.
ELR is ruled by guys shooting anything from 6mm to bigger .338s. I would think 6.5PRC/6.5SAUM type shooting the heavies is a great option for getting a high BC bullet up to good velocities without destroying your shoulder. Maybe a good 7mm or .308 based csrtridge, but they will limit your round count for the day. Unless you build really heavy and put on a great brake.
If you want the best of the best for 2000+ ELR, that is a whole other topic. .338LM, 375 ENABLR, 375 Cheytec, 416 Cheytec, 416 Barret, etc.