I will suggest leaving it 12v and replacing the wiring as needed. You don't have to buy a wire loom, just replace the wires as needed. The wiring on a Jeep is very simple and the wiring diagram in the manual will help a lot. Remember, it's not a Corvette, it's a Jeep. They are simple so keep it simple.
The starter is 6v but works fine on 12v if you don't hold the starter on for long periods of time. If it don't start in 15 seconds let it rest and find out why it didn't fire off. It needs spark, gas and compression to start and if one is missing it won't start.
If your going to use one of them as a daily driver or as something to knock around in DON'T restore it, just repair as needed. A totally restored Jeep becomes a Garage Queen and is seldom driven.
Save any good parts you replace, they may be better than the reproduction parts you buy. Only buy from a reputable dealer and try to stay away from buying parts on ebay unless you can trust the seller. If you have questions ask here, someone can help you.
Get the reprint copy of the original Willys shop manual and read it.
I suspect the shifter fork rails are rusty or frozen from sitting. Remove the floor cover and pull the shift tower and have a look see. It's not that hard to do. You don't need a new gasket, you can use RTV on the cover in place of a gasket. Just don't put a lot on, a little dab'l do ya, just like Brylcream.