Ridge Runner, Welcome, A scout mount for your rifle, whicheer you choose,will be a project that needs a gunsmith. It can be done, but a simplier choice may be to use a shotgun scope. It has a longer eye relief than a standard rifle scope and allows for easy both eyes open target acquisition and sighting usng the scope to look through more than as a sighting plane.
As to which chambering, obviously there are both good, and several choices. I would tend to ster you back toward the 30-30, not because it is a "beginners rifle" and I consider you a beginner, but rather, if you are hunting in the woods of Maine, I am not sure that you need the range or power of a 308 or 30-06. Don't over look it because it is an older, less glamourous chambering. These days the 270 is probably losing ground to cartridges like the 7mm Rem Mag. But it is an outstanding deer cartridge, and it's champion Jack O'Conner used it to kill everything on this continent.
Being in the Northwoods, it is entirely possible that yu may get an opportunity to hunt moose and the 30-06 loaded with heavy bullets would be more than up to the task. All of these, the 30-30, the 270, 308 and 30-06 ahve two things going for them, first the ammo makers offer cheap ammo that can be bought in the 2 months preceeding hunting season for CHEEP. Second, the ammo makers offer at least one if not 2 or more premium loadings in every one of these. What ever your choice, I am sure you will enjoy your Handi.
Hang out with us a while, we'll get you hooked up with 2 or 3 maybe 4 Handi's, get you to handloading, and in general fix it so that it will be impossible to pass a gunshop without the owner grinning like a mule eatin' briars. Good to have 'ya aboard. JP