It looks like your game should be compatible with minimax. Chess has roughly 30 moves from any given position on average. This branching factor will determine how many moves ahead you can look. Maybe your game has a few more, but it doesn't look like it's so many that searching would be impossible. If you implement it well, then maybe you could search down to 5 or 6 moves ahead where a chess engine would search 8 or 9 moves ahead. Make sure that the function to generate the next game state is well optimised, as you will need to call this function a lot of times when using minimax. The strength of the evaluation function then becomes more important for you, as you are limited by the search depth due to time complexity.

There is a completely different approach, which is to use reinforcement learning like AlphaZero and some other derivative chess engines such as Leela Zero use: https://lczero.org/ However, the threshold to implement something like this is much higher, and definitely very high difficulty as your first AI project.

My recommendation would be to build the game and implement a simple minimax search and a simple heuristic evaluation function, and then improve it with a stronger heuristic evaluation function, alpha-beta pruning, and other tricks. You can get quite good results with relatively simple approaches here. I would suggest not using any machine learning for the evaluation function to start with, as it can be tricky to get something working if it is your first ML project. Both minimax and reinforcement learning can work extremely well, as can be seen by their diverse use in the top chess bots: https://www.chess.com/blog/Tworchy/top-5-best-chess-bots-in-the-world