I have recently been picking up the guitar and started singing after a very long break. For quick demo recordings, I got a Tascam DP-006 - a 4-track recorder that uses a SD card instead of tapes. It also comes with a set of built-in stereo microphone and can run on batteries.
I have great fun and have been making recordings quite frequently with this 4-track. They won’t be good enough for serious recordings, but should be more than decent for quick ideas and demos. Highly recommeded.