Every airline has different policies and scheduling practices, so it is impossible to generalize. You might have to work anywhere from 14 to 23 days/month. Those days may be in several short trips or 1 long one. Some schedules may get you back to base many nights; others will keep you away the entire trip.
Leave policies also vary. However, you should understand up front that few airlines will put up with repeated requests for personal leave - paid or not. After all, they hire pilots to fly, not to sit at home with their kids. The first (probationary) year at any airline will be the worst, since you will have to tread lightly or face the wrath of your chief pilot.
Living at your base will make it a LOT easier, since you won't have to spend an extra day before each trip trying to jumpseat to base.