for push with key into ignition this is how i would wire it.

wire push button, ground to button, button to relay make sure when button pushed, ground is present

Relay terminal 85 to ignition
Relay terminal 86 to push button (shows ground when pushed)
Relay terminal 87 to Constant 12volts Fused with 30 amps.
Relay terminal 30 to start wire, Motor side.

when ground is prsent, relay allows 12v to the starter, once it has started u MUST LET GO, this is not a button that will auto detect ur car is running.