Warming up before exercise

I never know what kind of exercise or stretching is good for warming up without getting tired before the actual routine begins.

I generally start out with about 20 mins. of stairmaster. By the time 20mins. pass, I am beat. I have literally no wind in me for weights and strength exercises. I do a few and then I am ready to collapse. Should I just do 10 mins. first and do the next 10 mins. after weights? I have tried that and am never happy or motivated to go back to stairmaster after weights. So, I just leave weights for last.

I have some readers trained and certified in fitness. Hope to get an answer from one of you.