I would split the body, yes. I would do sprints sometime during the week (outside!) but not on the weekends as it will hinder your leg workouts. No need to worry too much on bis and tris if you're doing pull ups or chin ups and push ups or bench pressing. If you're new to lifting I would suggest heading over to Stronglifts.com or checking out "Starting Strength" for great and simple to follow guides on lifting, routines, sets, etc.