I would say a hybrid with a rigid fork. The ones with suspension forks on them are not meant for going off road, but a rigid fork will do just fine. You can change out the tires with some cyclocross ones for when you want to hit some dirt, just don't expect to hit the really hard and technical trails!
As for cost, find out what brands your local shops carry and check out their websites. A $350 hybrid will have the same frame as a $700 hybrid, but the components will be vastly different. My advice is always buy as much bike as you can, since the bike companies get the components for much less than they would cost after market. Buying a bike only to plan on upgrading later is the more expensive route, especially on a bike where you likely won't be breaking parts with the type of riding you plan on doing.