I have to go along with several other posts and recommend the .25-06, it is an ideal cartridge for deer-size game. I have one, a Howa 1500, but that rifle is probably too heavy for your liking.
It also seems that you are leaning in the direction of a short action rifle, which will lighten up the weight a bit since they usually have shorter barrels and may be available in compact stocks.
So with that in mind, and knowing that you don't reload, (you should, it would really open up some options) I recommend in this order: .243 win or 7mm-08. Most other short action cartridges under .308 bore dia. are going to be a little harder to find ammo for.
As for the rifle, a Winchester featherweight, Savage 11 lightweight hunter or older remington model 7 are good rifles, among others