You might want to try one (or more) of these alternatives:
This is what I use for warmup. My favorite is the bear complex. The video is worth a million words, but in short, you start with the bar in front of you. You power clean it into a front squat position, do a front squat, push press it into a back squat position, do a back squat, then push press it back to the floor in front of you.
I use a relatively light weight, because I do typical 8-12 rep weightlifting exercises afterwards. However, you can use slightly heavier loads to mix cardio and weight-lifting at the same time.
In circuit training, you do one set of one exercise, then immediately do another set of a different exercise, etc, until you're back to the first exercise, then repeat. For example, you might do one set of squats, then one set of bench press, then one set of pull-ups, then one set of standing press, then squats again, and so on, until you've done 3 sets on each exercise.
Typical weights+cardio solution
Another alternative is to do a typical weights training program which lasts 45-60 mins per workout, like Starting Strength, and add 30-45 mins of cardio after. This separates the weights and the cardio parts, but it's what most people do.