A cyclocross bike would be perfect for you.
A cyclocross is essentially a modern road bike with a bit more clearance, stronger wheels, and nobs yet relatively thin tires. In my opinion it is completely superior to the hybrids, which are simply mountain bikes without shocks equipped with slicks. The cyclocross bike has drop-bars/hoods which are extremely comfortable to ride, and let you get nice and aero if you need to fight the wind, unlike a hybrid. I though I didn't like drops till I commuted in flat, windy desert for 10 weeks, then I loved them like my own mother.
Entry crossbikes to check out are the Fuji Crosscomp (got my 05, first, worst year, for 450 with a funky rear rim), Kona Jake, Motobecane Fantom Cross, and older Kona Jake the Snakes. Any of these will run about 500 used, 800 new. I think there is also a cannondale or two that is bellow 1000 new. Specialized tri-cross and bianchis tend to be more, but check with a shop.
Cyclocross bikes are designed for mixed rides on dirt track and road.
If you can't afford one of those, I have heard that if you take a 70's road bike with good clearance on the breaks, you can fit cross tires on and turn it into a sort of cross bike. You could probably do something like this for 250-300, but I'd just spring and get a real cross bike, because if riding a bike is a serious method of transport, there is no point wasting your money on a cheepo at the beginning. Tires may be expensive for one of these conversions, as most of road bikes have 26" or 27" wheels, not modern "700c", aka 622mm). At the very least you'll prolly have to buy them new, instead of at a swap meat for $10, the way i got mine.
If you want a hybrid, just get a cheap aluminum mountain bike, lock out the fork (or just get a frame with no suspension at all if you can), and put slicks on. I would go with an old school road to cyclocross conversion over this. It will be much faster and much more fun. Probably better quality too. Also it will do better on gravel than a slicked mountain bike (ie hybrid).