Definitely use a leather rope and also make sure it is long enough, good rule of thumb is that the handle should reach just below your armpits when standing on the rope. Your hands should be approximately a little higher than hip height when jumping.

Good advice, definitely keep it short if you are going to be doing bodyweight training every day. 20-40 minutes is fine. If you train 3-4 times a week you'll reduce your chance of over training.