The first cartridge I ever started loading for (at the end of the 1980s) was the 7mm Remington Magnum. The first handload I ever put together was 61.5 (or 62) grains of IMR 4831 behind a Hornady 162 grain BTSP. I didn't know it then but I had accidentally stumbled upon one of the all-time great loads for that cartridge. In fact, as the years went on, that load became the first I tried when testing a rifle in 7mm Remington Magnum because it seemed to be universally excellent. If this load didn't work with the rifle, then I figured there was a problem with the rifle itself, or the scope.
Depending upon the rifle, I've seen it give velocities between 2,950 to 3,050. It also shoots 1 m.o.a. or better, depending upon the rifle.
I found IMR 4831 to be a great powder for this cartridge, and the reloading manuals also recommend it. The other magnum powders (Reloder 22, H4831, N560 etc.) are also excellent.