Many people run after the lift, i find it to be the best time, and it wont eat away at the muscle unless you do tremendous amounts. I find 30 mins. to be best for me.

Essential:  Reverse the order. Lift first (warmup with lighter sets of the lifts themselves, as many as it takes), then run (sprints or high-intensity intervals, and no more than 30 minutes, if you want to build any muscle at all), then stretch (last).

Better:  Run and lift on alternate days; and don't run at all the day before or the day of a heavy leg workout.  That's the best way to mix running and lifting (which mix well only if general fitness, and not strength or physique, is your goal).

Running will burn fat better than anything else, for most people.  Unfortunately, it will also limit muscle mass gains, especially leg mass and strength (look at the starting line of your local 10K . . . that's where running takes you . . . are those bodies you'd rather have?), and risks injuries (60-80% of runners are injured at least once in any given year) worse than any other form of cardio.  Its a real balancing act to combine it with any kind of serious strength training or bodybuilding - which is why virtually no serious strength athletes or bodybuilders run at all, and the few that do use sprints and HIIT instead of steady-state "distance running."  

If bigger and/or stronger, but leaner and good heart health as well, is your goal, look at less catabolic, but still good aerobic calorie burning exercises like fast walking the incline treadmill, stepmills, circuit training, swimming, sled dragging or Prowler pushing, or stationary or regular cycling - for various reasons, those don't seem to "skinny you down" like distance running - which partly explains why serious strength and physique athletes DO use those methods of cardio.