i think you will be fine with whatever bike you decide to go with or even keep the bike you have. The rims are what you need to keep an eye on. IF you start breaking spokes, you might consider going to a stronger rim with more spokes.
And its great yo uare watching how you right. Thats the key I believe. But if you do have to go over a pot hole or off the curb, stand up on the bike and shift your weight a little back and it will take the preasure off your back wheel.