For someone who is wanting to play tunes 'out' you have chosen one of the most difficult instruments to 'out' on. I'm presuming from your initial list of instruments you can knock a tune out on, you are basically an ear musician like me. Each of the instruments you mention has different limitations. The anglo for instance is probably the easiest instrument to get to a passable standard on but unless you can play the complex illogical (to me) Irish style it can be very limited keywise.

Ah but, I hear you say, a decent anglo costs the earth nowadays. Not quite, I was in a session a couple of weeks back and a young man who can't have been over 20 was busking in very competently on a wide range of tunes on one of those new black things with accordion reeds.

If you want to 'out' as soon as possible surely the best place is a learner's session or even a medium session with friendly musicians. If there isn't one in your area you could consider starting one.