Hard to help someone that doesn't like the '06, (you've already ruled out the best moose cartridge on the planet) but I'll try. Nothing wrong with the 280 or 7mm and if those are two calibers that you are thinking of, I would imagine you're trying to avoid recoil. My son has been using a 308 with Federal's high energy loads for moose and handloaded 165 grain Hornady bullets for deer. He was 11 when he shot his first moose and has since used it for elk, black bear and mule deer. He's now 17 and has recently picked up a 338 win mag. Of the 2 you mentioned, I'd go with the 280, as it is bound to be lighter, shorter and all round easier to carry and shoot than a 7mm. A 280 is enough for a moose and if you use the high energy loads it's getting close to 7mm velocity. The only reason to carry anything bigger is if you're hunting in an area that has grizzly bears. Then I'd go with the 338 or 35 whelen.
Far more important than what you hit your critter with, is where you hit your critter. But it's nice to be able to break bone if your shot is less than perfect.
A good scoped 22 is a great way to practice your shooting without the wear and tear on your shoulder and nerves. Happy hunting.