You don't need to be ashamed of that Huffy at all. It served its purpose, and now you've just got to the point where you've outgrown it, or seen its shortcomings. Now you have earned the upgrade!
Whatever bike you get, though, won't make a really signifcant difference. It's the motor, not the bike. But, the more you ride, the more your body adapts to the demands you place on it, and a training effect takes place, even if you don't go that hard. So don't feel bad if you think there's no improvement. As long as you're riding, there's improvement.
As for the hills, I used to have lots of low back pain. It disappeared when I stopped trying to push too big a gear while seated. Now if the gear is too big, I just stand on the pedals and use body weight, arms pulling on/stabilizing the handlebars, and back leg pulling up slightly to drive the bike forward. If you're not used to standing while climbing, just start small and work longer as you get more comfortable.
L.