Thanks Anna! Why do you think the overhead press is better than the bench press? The load is much higher at pench pressing, like other said.
Whats your opinion on weighted push ups?
My goal is the maximal full-body strength.
OH press because with the overhead press you're supporting the weight with your whole body. But the bench press probably gives much of the same, with the greater loads and good use of full body tension and leg drive. Can you do both? I like the way the two are alternated with the Starting Strength program, at least for those with newbie gains to make. Past that and you really need more volume of each to make specific progress. Both can also be programmed in with StrongFirst's Reload program.
I don't have much opinion on weighted push-ups except that for most people the bench press will offer more precise load management and better range of motion. But if you don't have a bench and a safe set-up for solo training, I'd go with weighted push-ups.