You'll find about as many opinions on "what's the best cartridge" and "which is the best gun" as there are stars in the sky !
Most mosern cartridges ( and quite a few older ones as well ) between.243 and .45-70 are entirely adequate on deer ( and the 30 Carbine [M1] isn't one of them ! Those in the .270 and up range are also quite adequate for moose.
The New Model 7 CDL Remington's are great looking little guns. The .243, and even better, the .260, would make very nice light rifles for what you've stated you need. If moose were to be in the mix, I would opt for something a little heftier, a 7mm-08 or .308. Or, if you really want a neat heavier cartridge, which will certainly work for moose ... try the .350 Remington Magnum. Keep your choice of scope to 1-4x or 1.5 - 4.5x and you will have an effective combo for the heavy stuff. PLEASE, no 3-9x 's !!!!
Nothing wrong with the Marlin 45-70 you mentioned either, but my preference would be for the longer barelled model.
In the end run, it's going to be you who has to choose !
Pumps, levers and semi's seem to dominate the eastern deer camps, with bolts being perhaps a little more popular amongst the moose hunters. The bolts, pumps and levers are often regarded as the more accurate and less trouble prone, but semi's if kept properly cleaned and well-maintained will provide good service.