Our old JD 530 gas tractor sounds a lot like yours. The ignition switch just turns on the ignition. There is a starter button to crank the starter.
All too often, I see folks who start re-furbishing old tractors get hung up on generators and voltage regulators until the whole project loses interest. Here is an alternative:
If just starting out with yours I would go buy a good 12 volt AGM type battery. Charged up by a trickle charger overnight, that battery will start the tractor dozens of times if not more.... and also run it for ten or twenty hours easily and give you enough lights to drive home as well. You can plug the battery into a battery maintainer type of trickle charger when not using the tractor. Lots and lots of farm tractors work just like that for years.
Replace or inspect the battery cables to the frame and to the starter. You will probably need new battery post connectors at least. Amazon ones are about $12.00 a set. Pos and Neg battery terminals are different sizes!!
Then get a carb kit or just the float bowl parts. I use steinertractor.com. Take off the carb float bowl, and replace the carb float, needle, and seat and the bowl gasket. That's all for now and will cure the leak. Before starting this, make sure you can turn off the gas to the carb when working on the carb and always when not running the tractor. If there isn't a finger valve to do that in the fuel line to the carb then add one.
Replace the points, plugs, and particularly the distributor cap and spark plug wires. Of these things, it is often the spark plug wires and ends that make the most difference. Clean up the old spark plugs and reuse them for now.
Done...
good luck,
rScotty