Depending on the degree of sophistication required (it's a very deep rabbit hole...), I would suggest that excellent results can be obtained with a large-diaphragm condenser mic. Budget determines the choice, really; there are fine mics available for £30-40 which do the job very well indeed. I'd assume that these would be used in conjunction with an audio interface, such as the ubiquitous Focusrite Scarlett 2i2 (around £125...) or similar, to adapt the signal to the PC running the DAW, and to provide the 'phantom' powering that these mics require. That particular interface has two mic inputs, so the option of a second mic becomes useful (the large-diaphragm for the body of the recording, a small-diaphragm mic oriented rather towards the neck for some detailed sound; other mic placements are available...). A similar cost, starting at £30, gives a wide range of possibilities.
Which models, in particular..? We have successfully used Superlux mics (Superlux E205; Superlux HI10...) for this kind of recording, and, for home/semi-pro work, would look no further for value for money. Spending more may provide other options, such as built-in filtering, or adjustable recording 'lobes'; I tend to a rather minimalist approach. It's worth looking into, and experimenting, with both mic placing and room choice, as these have a wide effect on the results.
Disclaimer : Subject to completion, correction and/or contradiction from others. Hope this helps.