cardio or weights which
I, too, have each and every one of my clients do approximately 10 minutes of warm-up prior to stretching and then we hit the weights.
As far as cardio goes, I advocate doing cardio on a different day or at least at a different time, if it is necessary to do it on the same day. There are a couple of reasons for this. First, you want to utilize all of your stored muscle glycogen to fuel your workout. It will enable you to have a stronger workout. If you have expended it all doing cardio, you will feel kind of shot during your lifts. Secondly, I like to have my clients use cardio as a conditioning tool. That being said, I will have them do HIIT cardio on one day and steady state on another. Both of these require maximal physical output and you need the fuel you have stored to perform proficiently.
There is another reason for having clients do cardio and resistance training at different times. That is to maximize the amount of body fat they can burn during each particular type of exercise. During resistance training, you are firing up your metabolic rate substantially. It will be on “afterburn” for hours after you are done. You will burn body fat during your cardio sessions, as well, but within a short time after finishing, your metabolism will return to normal. Splitting up your sessions will allow you to get the greatest benefit and fat burned from both types of exercise, without ever starting to burn muscle.