For singing online, a good quality USB headset works well. We recommend the SADES SA902 gaming headset.
For instruments like pianos, cellos and violins, a condensor microphone is a good choice. In this case you will also need to connect stereo headphones to the microphone itself.
For electric instruments such as electric keyboards, synthesizers, electric guitar, or electric bass, a USB audio interface is required.
In this case you will also need a microphone and headphones.