Crossfit rocks. It won't make you look like a bodybuilder, it will make you look like an athlete...because you'll be training athletically. If done with dedication, crossfit will harden your body. You'll get stronger in virtually every way. You will build muscle, just not superfluous muscle.
If you choose something other than crossfit, definitely do lift. Center you workouts around compound movements, e.g. deadlifts, squats, cleans, bench, pullups. Isolation movements, e.g. curls, tricep extensions, lateral raises, should be supplementary.
Someone mentioned high intensity interval training for cardio, and I second this. It will quicken you metabolism more than long slow cardio will, and won't cost you any of the muscle gain from lifting that long slow cardio sometimes can. That being said, long slow runs are still good for you.
As for losing fat, diet is more important than virtually any workout. Think in terms of nutrient value per calorie. By that I mean ditch the junk food and booze. Get as many of your calories as possible through fresh salads, steamed vegetables, fruit, legumes and lean meat. Avoid as much processed food as possible. Supplement your carbs with a little brown rice or sprouted grain bread. The zone diet is a very good place to start your diet research.
Good luck and have fun!