It seems that 2 player games usually require more buttons than 4 player games. Am I correct?
Yes. I think someone posted that no 4 player games have more than 3 buttons per player (except for some obscure mahjong game) If any 4 players have more than 3, it would be news to me.
I definitly want to support neo-geo games and street fighter games. Which leads me to using a 7 button layout for players 1 and 2. Am I still on the right track?
Right.
I'll include a track ball and spinner in the center of the control panel along with 2 mouse buttons.
Why do that? Just use buttons from one of your other controls. You said you wanted to conserve button usage... so conserve!
I'm not sure how many buttons I should use for players 3 and 4. I do, however, want to minimize the number of buttons used but still make it the button layouts as close a possible to as many arcade games as possible. How many buttons will that be and what pattern should they be in?
Like I said, no more than 4 for the 2 extra players. Any configuration will be fine. I would make the controls comfortable, rather than accurate to one game. Strait across would be my guess. Some use a diamond pattern. Either way, you have to make sacrifices. MANY games used special patterns, so really it comes down to ergonomics, user interface, and aesthetics.
One last question, what other function buttons should I include besided the obvious player and coin buttons?
Player one, two, three, and four. Get a coin door with four coin inputs rather than coin buttons. You can always set the individual games on free play in the 'tab' menu. If you are going for some kind of arcade experience don't use 'coin input' buttons. Half the fun is pumping in quarters before the countdown is up. Don't bother putting in admin buttons, you'll have so many buttons on your cabinet already, it would be a waste to add more. Just use an ipac or keywiz with some type of shift function. You mentioned saving buttons, so keep the number to a minimum.
As far as great layouts, take a look at the examples page here on the site, or do a search in the message board. We've had lots of discussions about admin buttons, number of buttons, players, etc.