Either one of those kits will work, they're both a universal style.
As for the electrical part. The stock choke does not use 12v for power.
You are correct, the choke's electrical connection gets connected to the "STA" terminal of the alternator. That terminal supplies 6-7 AC volts for power.
Originally, on the '73, the alternator wiring harness has a white w/ black trace wire that goes directly from the choke's coil to the "sta" terminal on the alternator. If that wire is gone or damaged, just run another wire.
Here is a picture of a NOS '73 alternator wiring harness. In the first picture the long white wire (actually white w/ black trace) that is taped goes to the choke housing. In the second picture the other end of the wire is hooked to the "sta" terminal of the alternator.