I would recommend either a guitar or piano since they are both popular instruments for singers to accompany themselves. Guitar is more portable than a piano for sure but pianos will let you play songs that would require two guitars to pull off.
you ideally need an instrument that lets you play chords, so it normally comes down to guitar or piano, as @Chris82 already said. while ukulele or accordion are also possible examples, they are not as flexible and not as widely used
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