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*