This is wise advice, although I would not recommend never doing weight training, but you REALLY need to fight the desire to max out. I started lifting my Senior year of high school, and continued through the army and through college, etc. I've been weight training for 15+ years now.
I highly recommend doing body weight, and LIGHT weight training, accompanied by daily stretching and some form of activity. If you've been a little heavier your whole life, then you have to take it slow and let your body adjust. Work mainly on form, with any exercise. Doing 25 smooth and rigid pushups is far better for you than slamming out 50 sloppy half push ups. I also highly recommend working your core almost daily. Bigger guys often neglect this and its detrimental to their performance.
Fight the urge to look like you're doing something awesome, and instead focus on bettering your mind and body, and understand it will come with time. Injuries and sub par results just aren't worth it.
Regarding your shin splints. I think you just need to go less distance, and give yourself time to adjust, but I don't recommend stopping. This is also where your form is important, even for walking. Most people walk onto their heels. Either way, just listen to your body and don't stop.