The ideal way to warm up is not to stretch, not to elongate… but to rotate. Rotation can encompass movement and warming of the rotator cuff (the grouping of muscles and tendons in your shoulder) as this muscle is very prone to injury and is pretty much used in any upper body work-outs.
I would also suggest that some kind of lower body warm up. I have begun to incorporate some burpee’s straight after a low intensity, steady state cycle (duration approx 5 mins). I have found this is sufficient as a warm up.
In the past I have been guilty of doing a warm up that was relatively intense such as a HIIT cycle session for 10 mins followed by around 100 press-ups (5 sets of 20 reps). This certainly did ‘warm me up’ but perhaps a little bit too much. After all you need the fuel in the tank for the session, not use at least a quarter on the warm up!