Action figure photography has exploded as its own sub-genre in the last few years. There are some truly amazing artists out there. You can find most of them on social media.
With that in mind, each one of those artists will recommend a different method. You simply need to pick a place to start and then develop a technique that works best for you.
For my part, I employ a variety of lighting implements, mostly LEDs. Some are small, general are lightz on tripods, others are pucks that can throw light on backgrounds. I still use a couple of old flex-neck desk lamps with 5,000 K fluorescent bulbs. (I turn them into spotlights using old Solo plastic cups.)
As for the camera, I’ve upgraded to a Nikon SLR. Makes a BIG difference from the point-and-shoot days.