I think if you want it mostly to accompany yourself singing, you ought to try guitar first. It's more flexible than banjo or autoharp - you can take it in more different directions.

You should be able to accompany yourself, singing three- or four- chord songs in the "peoples' keys," within a month or 6 weeks if you allow half an hour a day for practice.

Just one opinion - and doubtless biased.

Peter.