Pull it, carry it or put it over your head. Those are the basic lifting movements. Deadlifting, one of the most, if not the most useful overall exercise is a pulling movement and there are many other variations and exercises that pull, like rows.
The flip side to that coin are pushing exercises, like military presses, push presses and jerks.
These, like the pulling movements are also compound, thus highly beneficial even though the weights handled are considerably less. They require healthy shoulders to perform and some have mistakenly claimed that you should not do overheads past the age of 35. At 53, with formerly battered shoulders, I generally disagree. Of course, in life, there are some limitations and plenty that can go wrong with the shoulder joint so maybe what you need to do first is rehab those relatively delicate joints with mobility exercises as advocated by the likes of Pavel and Eric Cressey.
You may need to learn or review the proper technique of overhead pressing before you think about increasing the weight on the bar. Adam, at Mens Garage has a valuable checklist of pointers you will need to know and master.
There are a variety of implements to press, so try them all from barbells, dumbells, kettlebells, sandbags, strongman logs and even big rocks. But be cautious of your shoulder training. Crossfit trainer, Steve Serrano says you need to “treat your shoulders like glass”. My own shoulders went from being my weakest link to…not. (I have plenty of others?!
My distance running running girlfriend, Val, also loves the overhead and she says her overall strength has improved as has her mobility and core strength. She also noted that her posture has improved as a result of doing dumbbell presses and dumbbell squat thrusts.
Mix up your overhead work and make them an integral part of your lifting regimen and do I have to remind you to ignore the shoulder press machines in the gym?