There is a mantra of "do which is important first" which is fine unless your goal is fat loss. Since strength training is more important than cardio for fat loss I do not see it as a preference thing regarding importance.
I am of the training school which says do them separately unless you are training as a runner. When I was coaching track and field, cross country running and cross country skiing workouts were always stated with the strength workout which I never found to degrade the later cardio work.
For general fitness doing three days a week of strength training and cardio on non strength training days is the way I structure programmes for my clients. Cardio as a warm up for strength training does not activate the muscle you will use for the strength training so a better option is to do bodyweight exercises for your warmup or use very light weights for the first set of each exercise. Do not include this set in your total for the day since it is a warm up which you record separately.
It is called WORK-ing out for a reason.
I said getting fit was simple, I did not say it was easy.
Cardio burns calories, strength work burns fat.
Eat well to lose weight, exercise to get fit
You can not build a six pack using twelve packs
Often when we seek a magic bullet for fitness we end up shooting ourselves in the foot.
"I think calories are little germs in food that all moms are afraid of" Dennis the Menace