if you have never ran i would start off doing a light 1/2 mile jog and see how you do. from there you can adjust
you can mix in a 1 mile run with your weight training days.. great for your heart health. do the weight training then go to the park and run 1 mile and try and beat your time
and also you better make sure you buy proper running shoes. don't think you can buy $15 walmart shoes and run on them. the wrong shoes will cause major problems