I started in my late twenties. As @WeAdventure said, an incremental approach is needed.If you start with a mile, that's great! But if you have to start with 100 yards of running, or even less, between rests, that's just as great. Figure out how much is realistic in a run and then in a week or month. Then you can ramp up from there. Running is for the benefit of you, so let your own abilities and needs define it for you.
I personally track my running distance in a shared spreadsheet with friends, so I keep myself honest about my numbers. (This approach works great for us for many, many goals, turns out.)
It's very important to find your own way in this. A lot of people find some running gear or plan that they think sounds cool, and then they stick with it to the point of injury, even if it's not best-suited for them. So with new shoes, new running-companions, or new routes, start off being cautious as heck.