I started jogging back in 2008. There was this great little green-belt/power line/paved trail thingy close to my house (not close enough to walk there though sadly). It was 1.6 km from one end and back, but there was at least 1 other trail that looped off about the main path and back that was around 320 meters long. I used to walk/jog it and take the loop going and then just head straight back. I started out only being able to jog for about 30 seconds (I timed myself) before having to walk for about a minute to catch my breath and then jog for another 30 seconds. The whole exercise took between 35 and 45 minutes. I did it -every- day during the summer, when it was the hottest (b/c I'm stubborn sometimes), always trying to better my overall time from the previous day. In just under 3 months I lost 29.8 pounds and 17 inches overall. That was my only exercise and I coupled it with a low cal diet (1300 calories). I started at just around the weight I am now, maybe a bit heavier, close to 260 and finished just shy of 230.
It CAN be done. I did it in really old, but very good, Nikes and I never had a problem. The absolute WORST thing to happen though is a knee injury. Five years ago I fell of a side walk (honest to God); I slipped off it and came down with all my weight onto my right knee. I didn't get a chance to brace myself at all; and the person that startled me and caused me to slip didn't even offer to help (grr!). I damaged the bursal sac in my knee and ever since, I've had serious problems with that knee. It's something that just doesn't go away. One small, wrong move, one small weird shift of weight sets it off again and I'm in pain for several days. It's why I can't do any squats or lunges.
So, advice, would be to be VERY careful with your knees. Make sure you're running form is proper; back straight, shoulders squared, and you're stepping down properly.
And take it slow. Push yourself, but don't over-do it because then it doesn't become fun and feels more like punishment (at least to me it did).
By the end of the 3 months, or nearabouts, I had increased my endurance from 30 seconds, to 1 minute 30 seconds. I was quite pleased. But then we had a really horrible heat wave, my asthma acted up b/c of it, and my dog (well, parent's dog sorta) whom I had staying with me had heat exhaustion repeatedly (she already has epilepsy) so I ended up having to stop because I was worried about her safety during the day and worried about my lungs b/c of my asthma.
I never did get back into it
But I did enjoy it!