Which upper body exercises, such as push-ups, biceps curls, etc., are better for not enlarging your neck muscles?

There r some, but... Curls will build biceps muscles on flexion, and triceps muscles with slow extension back; there are various nautilus and other exercise machines that will be rather specific for biceps and triceps; however it's better to think in terms of what group of muscles r used to hit baseball, tennis, or golf ball, shooting hoops, pitching, all require using all upper body muscles for prime performance.