Almost everyone has problems when they first start running, and these become worse the older you get. The good thing, though, is that most people can work through the initial period if they do it right.
I was a runner on cross county and track teams in high school, but basically went thirty years after that without running regularly. I would often start up for a few weeks in the summers, then peter out. As I aged into mid 40's, found that I was getting injuries when starting out, and they didn't go away. I tore my calf muscle at age 45 (trying to imitate Usain Bolt), and that injury stuck with me for several years; I thought I'd probably never be able to run pain-free again.
Then a few years ago (2011) I started running and took everything more slowly, both mileage and pace. I actually started out just doing hikes in nearby mountains, since my calf injury made running painful but hiking/walking was fine. I ran a little bit later that year, things went okay but I still caused myself some injuries because I always wanted to try and run faster. The same thing happened in 2012, although I ended up running my first marathon late that year. It was painful and my persisting Achilles/calf injury was always present, at least in a small degree.
In early 2013 I started running again and threw all thoughts of fast pace out the window, and paid close attention to pains, backing off and sometimes taking time off until some niggling pain went away. I started running more often, five or six days a week, which paradoxically helped. Yes, you generally need more recovery time as you age, but if you keep your runs on the slow side and don't tax your body as much, running every day can be easier and more injury-free than running just a few times a week. I have talked to others with same experience.
I ended up qualifying for Boston Marathon last fall, proving that you don't need to train fast or hard to race fast (in fact best training for marathon is much slower than most people think). And this year I've run the Boston Maraton, a 50 mile mountain trail race, and I'll be logging well over 2,000 miles for the year (i.e., averaging 45 miles per week).
I have heard similar stories from many runners I know. "Injury prone" is very often a tag that attaches to any person who tries to start running too many miles or who tries to run them too fast. Since most people try to start running that way -- trying to do too much too soon -- most people end up being "injury prone".
Instead, start out slow, walking most of the miles if you want, and ramp up very slowly. I've gone from being injury prone to being injury free, mostly because I know the sorts of things that would cause me injury and I avoid doing them. The good thing is that once you've slowly ramped your body up to a given level, say for me 50 miles/week at pace around 9:00 to 10:00 per mile, my body is rock solid. I'd have to be careful if I wanted to increase mileage or speed, but if I just want to keep running at level my body is acclimated to the odds of injury are very low. And the pleasure when running is very high.