I am a handyman for my regular job. Depending on the state and what types of projects you take on, you likely don't even need a contractor's license. You *should* have some kind of liability insurance, and that tends to run $70-100/month.
I love that I get to fix things and make people's lives better. I have found that if you're reasonably good at "putting things right" (often a problem solving skillset + plus a knowledge of how to use various tools), and you show up reliably, the customer base is ginormous. Everyone seems to be looking for a good handyman-- contractors/etc. in this type of industry are _notorious_ for not showing up on time or shoddy workmanship or both. (I charge $50/hr, btw)
As far as getting paid, most people are happy to write me a check on the spot, or they'll use venmo to do an instant transfer.