HiLetgo Game Joystick Sensor Game Controller Sensor JoyStick Breakout Module for Arduino PS2 Raspberry Pi

Wired. It's much easier and can't provide power wirelessly. Use two of these 2-axis joysticks https://www.amazon.com/HiLetgo-Controller-JoyStick-Breakout-Arduino/dp/B00P7QBGD2 Mega2560 has tons of I/O; shouldn't be a problem.