A decent 2x2 audio interface (such as an M-Audio or Line 6) will allow you to record vocals (mic) and guitar at the same time. I think the M-Audio device is circa £130. You may have something that already does that job.
A DAW package (I use Reaper) can be use to record. Reaper has a free trial period (unrestricted) for 30 days. Purchase price around £35.
If it helps I can document my setup for you to review.
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Guitars: Cort Earth Grand, Cort G250 RMS, Kimbara Strat Copy, Vester Strat Copy (Stage Series), Custom Build LP Style (By Steve Benford), 'Podcaster' Custom Build prize! (tele Style), Variax 600
Mac based recording and VOX AC4TV