You should be riding either a light hardtail mountain bike or a good “cross” bike. And you should have it modified so that it sits somewhat more upright than a stock bike.

So, what bike in particular? REI sells a nice little hardtail mountain bike called the Novara Bonanza ($549; www.rei.com). It has what you need: aluminum frame, good-shifting Shimano components, disc brakes, a good front shock. For something a little spiffier, Marin’s Nail Trail ($850; www.marinbikes.com) offers a swankier component mix and Marin’s excellent frame design. I’ve always thought that Giant bikes offer great value, and that company’s XTC-2 ($1100; www.giant-bicycle.com) is no exception. Really a lot of bike for the money; excellent frame, good components. All three of these are straightforward hardtail mountain bikes.
You would also be happy with an “urban” bike that doesn’t have the trail-intensive suspension of the bikes I just mentioned. Bianchi’s Boardwalk, for instance, offers a light aluminum frame and 24-speed gearing in a bike that can handle road, hard-packed trails, and commuting without the weight of a suspension rig. It’s $500 (www.bianchiusa.com). Really, this one might do the trick.
Whatever bike you get, you can have the shop make some adjustments for you. After a test ride, for instance, you might decide you want to be a little more upright. I wouldn’t go too far here; I don’t think it would do your back any good to be sitting straight up and down, with all the shock from road bumps coursing up your spine. But the bike shop can add a stem with a steeper angle, so the handlebars are farther off the ground. Also, if you opt for a mountain bike, have the shop swap out the stock knobby tires with something that rolls better but still offers good traction. Avocet’s Cross tire ($30; www.rei.com) is a good all-terrain choice.
Finally, you may want to look into a suspended seatpost. This will take up some shock without the complexity of a full rear suspension. The RockShox GPS post ($50; www.rockshox.com) is a good choice.