For accompanying traditional dance music (and I've done a lot of it, though English rather than Irish) I like DADGAD. DADGAD chords don't oblige you to include the major or minor 3rd - as is the case with all the basic standard-tuning chords - which makes it particularly good for modal tunes but also less cluttered for major tunes too. And you get the extra depth to the D chord.

DADGAD does tend to get a bit samey if you play it in D all the time (and play other keys with a capo and the same shapes), but it works fine in G, A, Em, Bm etc as well.

Standard would, however, be the choice if you wanted to use jazzier chords and emulate Peerie Willie.