you can use any of those ga you mentioned, the wires for the buttons have extremely small amount of power going though them.
and the coin door lights are'nt gonna draw much either you should be safe with just about any wire you can find.
EDIT: with the ipac you got 2 choices, 1 run the wire to both the coin switch on the door & to a button some where else.. OR run different wires to the coin door & the button.. and then assign both buttons "coin" in mame
both solutions work.. one is a physical (hardware, hardwired) solution.
and hte other is done in software..
if you use mame to assign it coin then you can always change it later to something else, but if you wire them together you'll have to open it up and physically change the wiring if you decide you wanna change it to something else.
if you have inputs to spare then i suggest going with the separate input solution and just telling mame that the button is also coin.