You can take something like this
Simple, convenient .
Take condenser shirts. Why do you need dynamic? We're not singing on stage. Soundproofing, headphones, pop filters, carpets there later, everything later. The main thing is the microphone. It's better not to skimp on it.
External sound card with microphone input, such as the FOCUSRITE Scarlett Solo.
A microphone, if you do this at home in an acoustically unprocessed room, I would take a dynamic one - Shure SM58 - a classic, but you can also do something like the Sennheiser e835. If you want exactly the condenser as in the picture, then you can look at the Octaves, but the capacitor ones are always sensitive and will catch a bunch of unnecessary sounds and reverberations if you haven't removed them on purpose.
Stand-crane, microphone cable.
Closed-back headphones, Sennheiser HD 215 will do as a budget option.
Well, that's probably the minimum set. The next thing on the list is monitors.