I think that if you are going to shorten the barrel to 16" or so, your best bet would be a .357 or a .44. If you need a scope, a fixed 4X compact would be all you need, even a 2 1/2 would be fine. Plastic stocks are the lightest, if you can get by using them, the plastic youth buttstock is lightest. If you don't need a scope, I'd go with a good peep sight.
I've mentioned it before, my lightweights are 1) a newer .44 mag, barrel shortened to 16", and turned down in diameter, with peep sight.
and, 2) and older H&R 58, .30-30. This has the light, tapered barrel. I removed the sights, used the one-piece "dead-nutz" scope mount with a leupold 4X compact, plastic stocks. It is a wand!
I went a bit overboard on both, I found a place that sells titanium bolts, and got two of the ones that hold the butts to the recievers!!
A similar .30-30 would also serve you well!!
Mark