you only need 1 positive and a ground per switch.
all switches can shre the same ground.
I only added the other positives to show you were you can get more places to solder if you screw one up
the left and right trigers would be best for you.
since they already have solder on them. just tin your wire and solder to the already made joints.
and send that monster of a coin mech back

and buy a simple mech.
can not find one? go to buy/sell/trade at the top mid of your screen.
post you need one. you will have one with in days