Here's a post from Glenn Pendlay, olympic lift guru from Wichita Falls Athletic Club in TX. This was his response to a guy who wanted to get a 300 lbs push press.
my advice on push press is to #1 get your squat and front squat up. thats a whole other thread, but its safe to say that you wont be push pressing 300lbs with the same squat numbers that you are push pressing 230lbs with. youll need strong legs.
when i push pressed 440lbs, i had done 770 for a triple on the olympic style squat wearing only a belt, and 606lbs for a set of 10 without even wearing a belt. rob mcadams push pressed 375lbs weighing about 200lbs, he squatted 400lbs for a set of 20 OL style with no belt, and did front squats with 440lbs and more wearing only a belt. its hard for me to imagine a 300lb push press with much less than a 500lb OL style squat done raw. im sure its been done by some freak, hell some freak out there probably push presses his max squat. but if your aiming for 300lbs on the push press, id aim for 500lbs on a raw squat done deep and a stance close to what you are push pressing with.
now as to training the push press itself... i would do them twice per week if you are no good at them, if your technique is bad. do this just to learn the movement. if you are skilled at them, cut it back to once. but do overhead work 3 times per week if you can. do a variety of movements. military press, push jerks, even snatch grip push press, and regular push press with the bar behind the neck. benching once per week wont hurt you, but if you bench too much, it cuts down on what you can do overhead, at least in my opinion.
a good workout emphasising the push press might look like this
5x5 on military press
3x5 on push press
3x5 on bench press
3x5 a little lighter on some other overhead movement, like push jerk, or snatch grip push press
start conservative, build.. and after 4 or 5 weeks change the reps or one of the exercises.
for variety, you can do complex exercises... for instance, on one of the days, you can use a weight you can do around 4 or 5 reps on the military press, press it for 3 reps then push press it for 3 more, for 3 or 4 sets.
or, if you know how to jerk, take a weight you can push press say 5 times, push press it for 3, then jerk it for 2 or 3 more... again for 3 or 4 sets.
these complexes are killers! dont overdo them.
thats basically it, get your squat up, and practice overhead work. its nice to see someone interested in my favorite upper body exercise. a big bench is cool, but there is always the equipment controversy. a big jerk is simply a thing of beauty to me, but there are always those who scream "its all technique" and dismiss the strength needed to do it. but a big push press, i dont know, to me, its just the absolute coolest expression of shoulder/arm strength there is. i think a big push press is a damn cool thing.