Studio equipment

The most important thing is to have a 'dead' voicebooth, so you don't hear any reflections. This can be done by using accoustic panels such as

Next you need a microphone! :) The TLM-103 is a widely used option. A bit cheaper but also a really good option is the TLM 102.

To be able to connect the microphone to your computer, you need an audio interface. You connect the microphone to the audio interface. The interface is usually connected via USB or Thunderbolt. Both options are fine.

Good interfaces are the Universal Audio Appollo Twin or (in lower price class) a Focusrite interface like the Scarlett od Clarett. There are a lot more options of course (RME is a good brand as well), but these are good options to start a home studio with.

Your computer is still in need of audio software. Options are Pro Tools, Reaper. Cubase or Logic. Pro Tools is the most used and has a free version you could try (Pro Tools First).