I am 50+ and started running two years ago. The Couch to 5K app may help you. I also do 'jeffing' which is a run/walk/run style of running on longer runs. So I run for 60 seconds and then walk for 30 seconds and repeat throughout the run.
I would recommend getting fitted for trainers at a running shop, to avoid injuries. You will spend around £100, but it is worth it. Decathlon is great for kit although I now have a wardrobe of more expensive kit as I do so much running!
I wear a running belt/pouch which holds my phone, keys, tissues and some money/credit card as I run on my own and sometimes stop partway through for a coffee. I also wear proper running socks to avoid blisters and a good sports bra. I also wear headphones as I find that a running playlist helps me. Some people listen to audio books or podcasts but I like music when I run.
I have always kept fit at the gym but had never run outside until 2 years ago. I just got the urge to try it and have been hooked ever since. My advice would be to run at your own pace, not worry about how fast others run, or what they look like, and find a distance that you enjoy doing. It might be 2k, 5k or 10k, it really doesn't matter.
I started out by running round the block and I am now doing the London Landmarks Half Marathon next week. But don't compare yourself to others, you may be happy running round the block twice a week, and there is nothing wrong with that.
In my mind I look like a slightly older version of Jessica Ennis-Hill but in fact I am pretty certain I look like a rather overweight middle aged woman stomping around the street, but I have stopped being self conscious.