If you're wanting to play and sing at the same time, I would think you'd find a concertina a little easier.
I play piano accordion and have on occasion tried to sing with it but it takes a bit more ooommph than the little 'tina. I also think a 'tina sounds better with voice and you can put in chords or a harmony.
Guitar would be my instrument of choice to sing with but I've also sung and played Geordie pipes which is a bit trickier, especially if you want to play a harmony while singing the tune.
Probably the easiest would be an autoharp - it can be as simple or as complicated as you want to make it.
By the way, I find the melodeon diabolically hard - I need to concentrate like mad to get the right note and there's no way I could sing at the same time!