Almost of that entire list that BadMouth gave below is bad data.
Most of them are 8-way (Battlecry, Croquis, All the Dambusters clones, all the Iron Horse clones, Ping Pong, Tutankham, etc). Some are later model japanese titles that support the whole jamma standard in test mode, but only use one or two buttons in the game itself and most of those require japanese language skills as well). Punch out indeed has a 4-way and 3 buttons but is largely unusable because of the dual monitor nature of the original game. 
The quick story on number of buttons to use with a 4-way joystick is 2, unless you absolutely positively HAVE to play Mouse Trap, in which case you need four. Nothing else in mame as of .78 actually USED a 4-way joystick and more than 2 buttons (and chances are anything they added since then that would require more than 2 would be some sort of obscure early junk title that no one would ever want to play).
Dual spinners is actually pretty darn obscure itself, only a handful of games use multiple spinners and some of those are really supposed to have paddles. A single spinner position and two 4-way spots will actually buy you a lot more games than that second spinner will (there are actually a few single player dualjoy 4-way games and quite a few two player simultaneous games that use four way sticks).
Back when the Maws website was up, I searched for games that used a 4-way joystick with more than 2 buttons.
There were only a few and probably none you'd miss.  However, you can always map the controls in MAME so that when both buttons are pressed simultaneously, it posts the third button.  Two is enough for classic 4-way games.
You could do the classic 4 way in the center with two buttons on each side of it for left or right handed play, but the buttons on the left could also double as the buttons that go with the first spinner.
Whether you go with analogue pedals or not depends on how seriously you take the games.  Just having buttons is ok for casual play.  Most people just mash the pedal anyway.  If you take the games seriously and want to make it as far as possible though, it will take an analogue pedal.  Pole position is particularly bad about squeeling the tires and losing time if not using analogue input.  It doesn't make much difference in some games, like Super Off-Road.
EDIT: found my original post of games that used a 4-way joystick and 3 buttons
(no dealbreakers IMO)
battlcry    Battlecry    Home Data    1991    .070u3    Fighter / 2D
   croquis    Croquis (Germany)    Deniam    1996    .068    Puzzle
   dairesya    Dai Ressya Goutou (Japan)    Konami (Kawakusu license)    1986    .036b11    Platform / Shooter Scrolling
   dambustruk    Dambusters (UK)    South West Research    1981    .092    Shooter / Flying Horizontal
   dambustr    Dambusters (US, set 1)    South West Research    1981    .092    Shooter / Flying Horizontal
   dambustra    Dambusters (US, set 2)    South West Research    1981    .132u1    Shooter / Flying Horizontal
   farwest    Far West    bootleg?    1986    .031    Platform / Shooter Scrolling
   ironhors    Iron Horse    Konami    1986    .030    Platform / Shooter Scrolling
   karianx    Karian Cross (Rev. 1.0)    Deniam    1996    .037b06    Puzzle / Drop
   lvgirl94    Las Vegas Girl (Girl '94)    Comad    1994    .067    Puzzle / Drop *Mature*
   logicpro    Logic Pro (Japan)    Deniam    1996    .037b06    Puzzle
   logicpr2    Logic Pro 2 (Japan)    Deniam    1997    .037b06    Puzzle
   ppmast93    Ping Pong Masters '93    Electronic Devices S.R.L.    1993    .087u4    Sports / Ping pong
   punchout    Punch-Out!!    Nintendo    1984    .030    Sports / Boxing
   punchita    Punch-Out!! (Italian bootleg)    bootleg    1984    .116u2    Sports / Boxing
   reikaids    Reikai Doushi (Japan)    Home Data    1988    .057    Fighter / Versus
   tenspot    Ten Spot    Thomas Automatics    1982    .134u4    Maze / Shooter Small
   tutankhm    Tutankham    Konami    1982    .033b01    Maze / Shooter Large
   tutankhms    Tutankham (Stern Electronics)    Konami (Stern Electronics license)    1982    .025    Maze / Shooter Large
   zerozone    Zero Zone    Comad    1993    .034b06    Puzzle / Drop *Mature*