Push works your triceps and chest more than abs. Also, you can specifically target yor chest or triceps by your push up form. Placing your hands farther away from eachother works your chest more, while placing them closer works your triceps more. Good luck.
Push-ups work your triceps and your pecs. Depending on the variation you perform, either muscle can be worked more than the other.
For biceps, I suggest doing hammer curls as it works the long head of the bicep. Do 3 sets of 6-8 reps of relatively heavy weight. Perform negatives for maximum gains.