Listen to Rusty. Even though I'm a MTB die-hard, your particular circumstances suggests that a cyclocross bike is going to cover more of what you want to try at a higher performance potential than a "hybrid" bike.
For 10 points ;) , I'll break it down for ya:
A road bike is the fastest and most efficient on-road, but completely unable to deal with anything on dirt. Its ergonomics is relatively stretched-out and hunched-over for aerodynamic efficiency. It is the choice for speed and distance. Consider it an all-out sports car like the Corvette.
A (typical) mountain bike is built tough for trails from smooth dirt to fairly rough/varied, including small drops, sand, and rock gardens. Its ergonomics is relatively upright for control and the ability to shift your weight around. However, a mountain bike is slow in both speed and handling on the road, even if you install on-road slicks. Consider it an all-out off-roading SUV like the Range Rover Defender.
A hybrid bike is built with the upright ergonomics of a mountain bike (for comfort and better visibility of surroundings), but with a lighter build roughly in-between that of a road bike and a mountain bike. It is often the choice of urban commuters. Consider it a cross-over SUV like the BMW X3.
A cyclocross bike is built closer to the hunched-over ergonomics of a road bike (it actually looks more like a road bike than the other types of bikes), but with a burlier frame, brakes, wheels that can take light off-road use. With road tires, it is very close to a road bike in performance. With cyclocross tires, you can ride on smooth trails, but you have to dismount over bigger obstacles. Consider it a rally-style car like the Subaru WRX.
So why the cyclocross bike over the hybrid bike? It sounds like you are young and ride for fun (as opposed to necessity, which would be the case for bike commuters), which makes comfort less of an issue than you think it is. The cyclocross bike is going to be faster in most circumstances, and amongst cyclistas, it is MUCH, MUCH cooler than a hybrid bike.