For the rotator cuff throwers ten exercises or Jobes exercises. Important to do these with very light weight, 3 lb weight for these. Want to make sure the movements are precise with these exercises. It is easy to get sloppy with these but want to make sure the movements are good so that the rotator cuff is targeted.
For the rest, I prefer Zottman curls to regular curls, important when the weight is being lowered it is done slowly. Tricep extensions, skull crushers, rows, dumb bell bench press, turkish get ups and the list goes on. I try to do 1 1/2 to 2 back side arm/upper back reps for every front side rep.
For core…planks and plank variations, adapted (laying on the ground) russian twist, lawnmowers, medicine ball throws (or if you don’t have a med ball a creative replacement can be used) can be very good for core stuff.
Back to the upper body…
Push ups and pull ups are hard to beat. When doing push ups try to keep the elbow tucked next to the ribs when going down, don’t want those elbows to flare out wide as that puts extra strain on the shoulder. When doing pushups and pull ups I usually have guys do them to their max rep everytime.
I would also add some explosive work…sprints and lateral jumps for example…which can be helpful can be done at home as well.