Have you ever shot a gun before? How much strength / tolerance for kick (the "backlash" of the gun you get, can be painful if you're new and get a powerful one)
But for all around use, I would reccomend a 30-30 rifle, good accuracy with decent range (unless you're considering sniping the poor fuzzy rabbits from 900 yards away!), not TOO much of a kick, relatively cheap.
For the brand... Winchester maybe?
Or if you are kind of weak in the shoulder area, go with a .22 cal rifle, I used to shoot those when I was 10 so you should be able to.
Oh, and maintinence... All you really need is a gun sheath (maybe 10 bucks tops) and that should be it. Unless you want to go all out and get a cleaning kit and tuning kit and stuff, but you dont need all that.
30-30's usually weigh like... 9 - 10 pounds maybe? I forget but it's something light like that.