This thread could also go in the Recording Equipment section, to where I think I’ll move it to.
Computer built-in soundcards are usually quite crappy when it comes to recording, specially because they lack proper (if any) shielding, which means you’ll get a lot of electromagnetic interference… The solution is to go digital outside the computer, for example, through usb.
So if you’re on a very tight budget the best solution might be an usb mic. There’s a logitech desktop usb mic for about $20 which has got good reviews. See if you can get one of those. I think it would be a good starting point. It’s cheap and it’s not money thrown out…
If you want to read a very long thread, here my quest for buying a mic to record my classical guitar: https://forum.audacityteam.org/t/budget-usb-mic-for-classical-guitar-recording-needed/12367/1
And the shorter version: https://forum.audacityteam.org/t/non-usb-mic-for-classical-guitar-rec-findings-conclusions/13464/1