How to sense several magnet position (X, Y) on an area of approximately 50*50cm.

I want to build a connected chessboard as a final project. The idea is to be able to monitor every chess piece move.

I would like to detect chess moves thanks to a magnetic field. I will have to implement a magnet on every piece.

My first concern is what sensors should I use:

-Should I use Hall effect sensor or Reed switch as the reed switch is cheaper?

-Can I imagine to use only 9 hall effect sensors X, Y axis to detect several magnets (9 chessboard squares with one sensor) and therefore reducing the price and the electronic design complexity?

My second concern is what microprocessor should I use: We have the atmega328p

I need to design a matrix of 8*2 to cover the chessboard. So this mean at least 16 I/O pins. At this I might have to add bluetooth communication and user feedback (to know what move has been played by the opponent). Is the atmega328p convenient for this job? In the case I’d like to use led to manage user feedback (16 more pines). Should I use bigger microcontroller or could I combine some of them?

And finally, The size of the PCB will be really big if I want to cover the whole chessboard. Should I mill several modules that I could connect through wires? Or, is there any other ideas?

Thank you for your replies.