kingmo said20-30min runs 3x / week can be used as a warm-up before your weight schedule. It will not cause damage. Just make sure you stretch before and after the run, and hydrate (drink lots of water) throughout to avoid cramps.
If you're new to running, try doing incremental run times. day1 = 5mins, day3 = 7mins, day5 = 10mins, etc. and gradually your endurance will build.
you do need to give yourself 1-2 rest days between each workout, so that your muscles repair.
Well I am new to running, 'full-time' you can say, so I wanted to like run then walk and repeat until I finish the 30 minutes until I build up and am able to run 30 minutes straight.
If you say repair then I shouldn't do it on off days? My aim is for the run to just be some cardio for me on off days to say that I did something.
Thanks for the serious responses guys!