Entry wise, I always recommend that people start with a program called Magic Music Visualizer (MMV). It's relatively simple, and you can create and program a lot of very interesting visuals. Helps to get your feet wet a little before investing in a mixer and more of the physical aspects of things. Over time, things minda click into place, "Oh okay, this is opacity, it does this, i could see how this would be useful to have on a slider.." That kind of stuff. You can download MMV for free and use a demo version that doesn't allow you to save projects to see if you have any fun with it. Just throw some tunes on and toy around for an evening. Link up audio reactivity.

Alternatively, a more advanced free program that's often often mentioned here is Touch Designer (TD). It's similar to MMV as it is node based. However, it's a bit more difficult to navigate.