If you are going to start incorporating lifting for the upper body into your routine there are a couple of general rules I like.
Mobility matters. Allowing yourself recovery time is very important. Foam rolling pecs and the upper back is great as well.
When doing bench press I prefer dumb bells over a bar. They allow for more shoulder mobility. When doing push-ups make sure you keep your elbows in by your ribs.
Also, I like about a 2 to 3 to 1 mix of backside work to front side. For example, for every set of bench press I would 2 or 3 sets that work the upper back (face pulls, rows ect). Don't be afraid to mix exercises up. One day a set of curls the next time do Zottman curls.
In my humble opinion adding strength in the upper body is great for pitchers. Simple thoughts on this: remember to work the small muscles of the cuff everyday, think small to large in terms of importance of muscles....strength is more important than size....don't trade mobility for muscles....recover, hydrate and proper lifting technique are paramount....incorporate rotational work into your upper body strength program.