A Zoom (brand) recorder in a living room with lots of furnishings will get you a reasonable quality recording. Use Audacity (the computer programme) to mix the tracks on your computer. If you have good microphone you can just plug it into the sound card.
1/ record a rough single take to a metronome or drum beat
2/ play that back into one ear, and play/record the guitar part.
3/ do the same for the voice.
4/ mix to taste. You can layer several guitar tracks to thicken up the sound and add solos. Same for the voice. Effects can also be added, a voice track through a PA with a bit of chorus and reverb.
If you need to synch stuff then tap out the metronome/drum beat before you start singing or playing so you can line up the peaks on the computer graphic when mixing.