I pretty much have to agree with everything here - arm strength is good, but arms are but a small portion of the overall strength equation. Having strong legs/back and using them as much as possible will keep you from overworking your arms, and body mechanics is a HUGE thing in my occupation (nursing).

My recommendations are the usual Big Three (Squat, Deadlift, and Bench Press) along with Overhead Press, Rows (any variety you like, I do barbell rows cause I have a barbell), and pullups/chinups. Ab work is always nice, but no need to go all Abs of Steel; your abs hold you upright, all day, every day, and as far as muscles go, are already quite developed on most people. It's just that most of us have a bit extra. . . subcutaneous tissue over top of them XD