resistance bands

Here are some exercises that you can try if you are getting into training over the age of 50. They're pretty good for any age, covering strength, core, and balance.
Bands are particularly useful for the core because they force you to stay as tight as possible and help to create tension in your body.
There is a reason that dumbbells, cables, and bodyweight exercises have been around for eons and are still used today—they work.
In all seriousness, the shoulder is a deceptively simple complex of muscles that serve a large array of functions, but here's how to maximize those muscles with only a few exercises.
If you're lucky enough to have enough space to create a home gym then make it the best one you can.