If recording from home, then computer-based recording is the most accessible. Memory and a proper sound card should be a concern when choosing a new computer.
There are many recording software programs to choose from. Some, like GarageBand, come already installed in the computer, but more complicated varieties (such as Pro Tools) are bought separately.
The microphone is a major player in good sound recordings. If there is anyplace where extra money can be spent, it should be on a microphone. A microphone stand will hold the microphone in position.
Cables will be needed to connect the microphone or instrument being played to the computer. This is usually either a USB cable or a quarter-inch cable.
A suitable room to record means a room where it is quiet and has little reverb. There is nothing like finally getting the perfect take---until that garbage truck grumbled by outside.