As far as bands are concerned, I always liked Planxty very much. If you want to investigate the ballad groups, you could do no better than the rough and ready Dubliners.The Brady & Irvine recording mentioned above is masterful.
If you would like to hear something more traditional (as opposed to neo-traditional) you might like Frank Harte's 'Daybreak and the Candle End' as mentioned above. A fine recording of fiddlers is Denis Murphy & Julia Clifford's "Star Above the Garter."
Here are a couple you might not hear from other Mudcatters...
Skylark - Claddagh Records and Trian - Green Linnet
All the best,
Dan