Are you just starting or thinking about C25k? Almost a year ago, that was me.
I'm approaching 50, and was a regular dog-walker who wanted a bit more exercise than riding for an hour once a fortnight. So with much trepidation I started The Podcasts... I was so embarrassed that I did the first few runs in jeans and trainers in case I saw anyone I knew. (I also had almost nothing in the way of sports kit, but being seen was the big worry... I live a small town where you chance of eluding public scrutiny is nil.)
Nearly a year later, I'm still running. I still have the same trainers (though not for much longer, I suspect) but have acquired a nifty little selection of form-fitting lycra, some sports socks and a top or four - and a £1 pair of magic gloves from the local Co-op for those frosty dawns. I run for 30-35 minutes usually twice, sometimes once and almost never three times a week. I even took my running kit away on holiday and used it. The furthest I have ever run is 4 miles - I lack the time and the commitment to do much more, and I also run with a (large) dog, which makes road running deeply unappealing, so I'm limited to footpaths away from traffic.
My rather dodgy back has borne up well: it needed a trip to the osteopath five months in, but that was to do with galloping around the countryside on a rather large horse while away on holiday. Other than that, no injuries: a bit of stiffness, esp after running on hard surfaces (rather than the more usual mud), and the odd bramble scratch, but that's been it. I stretch religiously after every run (and I stretch beforehand too, but that's to do with the back, not the running).
All I'm saying is that you can do it too. You might not lose weight (I haven't) but the weight you have will be a lot more muscular and less flabby. Running probably won't transform your skin, or reform your chocolate habit, but you'll benefit from the endorphin glow (mine generally hits when I'm in the shower afterwards) and just being generally fitter, more physically confident, less easily tired. There's a huge amount of advice and help and encouragement available on this website: I don't come here much any more but I visited a lot as I approached that dreaded first 20 minute run and it gave me a real boost.
Go for it! Stick to it! And come out the other side, running!