Start with G, C and D. In the key of G that's the 1, 4 and 5, and it carries a lot of bluegrass, folk and worship. Em is the next one songs ask for. The rest can wait until a song makes you learn them.
0 0 2 30 2 3 02 0 0 22 2 4 01 2 2 02 3 3 13 0 1 10 2 2 02 2 3 04 0 2 22 0 0 12 4 4 2These are open and low-position shapes, the friendly ones. Bluegrass players also use closed "chop" shapes higher up the neck for that percussive off-beat sound. Those come later, and your fingertips will let you know when.
Song in an awkward key? The transpose chart moves it somewhere your hands like better.
Chartless listens to whatever is playing and shows the chords live. Pick mandolin as the instrument and each chord comes up as a mandolin shape, and the tuner has mandolin targets too. The live chart is free.
More: chord finder · how to tune a mandolin · banjo chords · guitar chords · ukulele chords · all guides.