For a recording computer, the very first thing you’re going to want is a low-latency audio interface you can plug microphones into. These don’t have to be terribly expensive, but you don’t want to go too cheap. My favorite bang-for-the-buck interfaces are the Behringer UMC204HD or UMC22, but if you think you might need technical support better go with something like a Focusrite Scarlett.

Then, you need software that can use the low-latency ASIO drivers for the interface, which Audacity can’t unless you build it yourself from source code. The reason you want low latency is that it lets you listen to what you’re recording actually sounds like as you’re recording it, without a distracting delay between the sound in the real world and the sound in your headphones.

So, you need a DAW. Ardour is open source but it isn’t free on Windows; Reaper is a better choice, even though it isn’t open source. No DAW at any price is better than Reaper for tracking live instruments. It’s widely used in professional contexts. It’s also wicked fast, and the tutorial videos on YouTube are fantastic (Reaper Mania channel) and well-organized in practical use cases.

The main “drawback” with Reaper is that its built-in mixing effects prioritize functionality and power over appearance; you kinda have to know what each slider and knob is supposed to do (or look it up), and there aren’t a ton of presets to fall back on, even though everything you need is actually in there. It also doesn’t come with loop packs or software instruments like digital synths or sampled pianos etc. like more expensive DAWs do. But resist the urge to solve these “drawbacks” with money - there are tons of free and/or open source plugins and software instruments out there for the searching - look at Decent Sampler / Pianobook and Spitfire Labs for instruments, ReaPack for community-built Reaper extensions (especially the Tukan stuff), Kilohearts and Melda for excellent free utility plugin bundles (that duplicate things Reaper can already do, for the most part, but with friendlier interfaces).