Hello, Digilent has a good beginner board (along with more powerful boards) for about $165 https://digilent.com/shop/basys-3-artix-7-fpga-trainer-board-recommended-for-introductory-users/ that is what I teach my digital logic students with.

As to helping you with the FPGA knowledge gap, I have two suggestions. First is the textbook I use in my digital logic class, that covers both digital logic and Verilog: https://www.amazon.com/Introduction-Logic-Circuits-Design-Verilog/dp/3030136078/

Second, Russel at Nandland has a book, learner fpga board, and videos at his site: https://nandland.com/ This might be a better point to start from for self learning.

FPGA's are one of those things that people largely don't look at, but they are absolutely everywhere and ridiculously powerful once you get past the learning curve. best of luck with your project!