If you take scale like C major, there's a chord that goes with every note of the scale. On a piano this would be mean playing three note chords on the white keys only, all the way up. So for the key of C that gives you
C_major D_minor E_minor F_major G_major A_minor B_diminished C_major
Now here is the cool part: you can play those chords in virtually any order and they are going to sound good (although probably better to skip the B diminished chord, and also helps to start or end on C). It also works in the relative minor key, in this case A minor (still just white keys on the piano, essentially):
A_minor B_diminished C_major D_minor E_minor F_major G_major A_minor
Those chords are all easy to play on a guitar. It would also be easy to do this in the key of G major (E minor) on the guitar. They key doesn't actually matter, but those are easy for beginners. You can just number the chords 1 to 7, then pick any sequence of numbers, eg. 145623, or 4545261, and play it, and it will sound good, and you can make up a melody or a finger-picking pattern to go with it. For some sequences you might need to get a bit creative and vary the timing (eg. some chords will work better if you move through them faster than average, some you can linger on for longer than average), but you could make lots of good music from that alone.