Hi Aaron,
Welcome!
Depending on your weight and the weight you plan to lift, bodyweight exercises can be more strenuous than weight training. For instance, if you weigh 200 and do pull ups, thats is more intense than if you do pulldowns with 150 lbs. My approach would be to combine both body weight exercises and weight training. I think they complement each other quite well. If you're just starting out in weight training, focus on learning the correct way to do each movement. Once you feel comfortable you can start to slowly increase volume/intensity.
Also, walking or light stationary cycling is a good warm up for running. Once your muscles are warm you can do some light stretches. It's usually recommended to save your harder stretching for after your workout.
Good luck!
Doug