In regards to strength training, all sets are not alike. The length of recovery time between sets depends on the intensity (amount of weight) and the number of reps in each set. If you are lifting a light weight with many reps, the recovery time between sets should be lower.
As a general rule of thumb, we like to give ourselves 1:30-2:00 min for the longer endurance sets of 10+ reps. For sets targeting heavier weights at lower reps, say 5-9 reps we would give ourselves 2-3 min of recovery. As a general rule, plyometrics and body weight based exercises should only need around 2 min of recovery.
The difference in reps per set is due to a difference in objective. For sets of 10 or more reps, we are targeting muscular endurance. For the shorter sets, we are targeting muscular strength. For our training purposes, you should find a weight that induces fatigue for the assigned number of reps.
As far as the warm up goes, the Jump Rope and Step-Taps should be ample. That being said, everyone is different and you may not feel “warmed up” yet. It doesn’t hurt to add to the warm up, just remember that the purpose is to prepare your body for strength, not to add volume.