How do I know if a particular module is suitable for the microcontroller?

Question

Do it yourself

Check input/outputs? Or choose according to other criteria?

Answer 1

Open the datasheets for the controller and the module.
Look in the datasheet for the module for the interface type - SPI, I2C, UART, and so on.
Look in the datasheet for the controller for the same type of interface. If there is support at the hardware level - well, if there is no support - you solve the issue with emulation.
Compare logic levels - is it TTL or CMOS, whether the supply voltages match.
If one of the CMOS chips is for example 5V, and the other is 3.3, the second must be indicated if it is tolerant of 5V on its inputs, or a level converter will be required.
Compare the speeds of the interfaces - it is desirable to take the controller several times faster than the module.
A good book is Pei An, "Pairing Your PC with External Devices."