Some microphones require unique power supplies. Some are very low impedance and have unique physical connectors.
Most microphones that you'll encounter will use the standard modern XLR connector and will work fine with modern USB interfaces and mixers.
I bought a Reslo ribbon microphone which had a unique 3 pin connector and 30-50ohm output.
I had to change the connector to XLR and upgrade the transformer for <150 ohm output to make it suitable for modern gear.