For Internal doors where no security considerations are required a "Tube Latch" is sufficient. It is normal to fit a 64mm latch to door handles, and a 76mm latch to door knobs. This is because you require a little more clearance between your knuckles and the door frame with door knobs.
If you are fitting a lock with key to an internal door a 3 Lever mortice lock is normally sufficient.
If you are fitting a lock with a key to an exterior door a 5 Lever lock is recomended.