Rick, the first thing you should consider doing is to read up on what is available. There were several options for charging systems available for that engine, including the 2 and 3 amp DC, (part number 611116) the 3 amp DC, 5 amp AC, (part number 611104) 3 amp AC (lighting) alternator (611095) and probably a few others.
All of these units (and those not listed for other Tecumseh engines) generate AC, which is either rectified (making DC) via half wave rectifier, (a diode in the AC output) for battery charging, or use a full wave rectifier on a small panel for charging.
You can power incandescent lights (bulbs with filaments) with AC, although the 3 amp lighting systems do not do well with 12 volt head lamps. (Use six volt)
No, I do not have those part numbers memorized, although I did spend a few decades as an aviation electrician among other "tron" endeavors, so I have a dim grasp of the terminology. A great reference for this information is found
here.
As far as finding parts, some of the usual parts houses on line may carry some, but most of them are found on Ebay. You would also need the appropriate flywheel.
Alternatively, there were some 110 AC starter systems available as pointed out above, where you plugged in to the wall and started your machine. I doubt that is what you're looking for, but if you did go that route, you could use a smaller LiPo rechargeable battery, and run an LED lighting system.
[MENTION=51233]Dr. Shop Teacher[/MENTION] just went through a lot of this research and might be able to discuss what he found, or direct you to some sources.