Pushups only is bad, but pushups with pull-ups in particular are a great pair. I learned this in my youth when I found the Armstrong program to be particularly useful. [1] I would also take a moment to emphasize the importance of stretching in muscle formation and recovery as well as injury prevention. I'm serious about the stretching, at 5 minutes per muscle about 1hr per day is a decent start.
1. https://savannahstate.edu/cost/nrotc/documents/Inform2010-th...