I'm going to offer one of two dozen recommendations to check into a cyclocross bike. It will provide just about everything you're after and a great many come with disc brakes now if you're sold on those. (I commute on a CX bike with discs, so no complaints here.)

With any decent level of componentry you're probably not going to shrink the number of gears you have, unless you go fixed/single speed or find a bike with an internal hub. Otherwise the lowest you'll probably end up with is 24 (which is called typically 8 speed and then specify a triple crank, rather than "24 speed")...much lower than that and you dip out the bottom end on quality, unless you're buying used/vintage.

Word is that 8 speed will be going the way of the dinosaur soon as well.