If you want to experiment with FPGA, the Lattice iCE40 series is a good starting point. It's not super capable (but will be more than enough for your project), but it was one of the first with a solid open source toolchain and has a strong open source / open hardware community as a result. It's also quite cheap.

Check out the iCEBreaker project for a decent board to get going with, and some educational materials: https://www.crowdsupply.com/1bitsquared/icebreaker-fpga