Read this article on T-Nation
sounds like a good idea for you, if you want to do running instead of weights / wrist and all that.
Might want to wrap that wrist if it is real tender, lots of arm swinging when running.
I'm a "glass is half full" kind of guy, I'd almost be happy I hurt my wrist as an excuse to jump into the Running Man routines.
Jogging, and any kind of running, can get great results but most people just get out there and slog it out, enjoy the endorphins, make little progress. They get fit to a certain comfort zone then jog on for years with a fat gut. Any good field trainer would whip your ass if you got that lazy. Comfort zone is not allowed in athletics. The key to jogging or any running based approach is to develop progression, push yourself more and more. The Running Man article is great because it lays it all out for you.
Otherwise if you just started running with no plan you'd get mediocre results ... pretty good at first but then level off and go nowhere.
This is especially true of walking / running because we are evolved to run/walk efficiently, using little energy/fat because nature doesn't want us to.
Most people cannot run properly, make sure your trunk is steadfast and rigid, your arms must swing with your legs (you can ONLY run as fast as you can swing your arms, .: sprinters have huge shoulders), your shoulders stay square they do NOT swing forwards and backwards twisting to match your legs, your head is level and minimal bobbing up and down, your arms are at approx. 90-135 degrees and stay there (some like a bigger angle, just don't change the angle mid swing). Watch some top sprinters on video. Beware, even at olympic level, some people have pathetic form. So watch the champions.