Getting you through many Irish tunes will be (depending on the tune of course)
Em/D

Am/G

Dm/C

You can spice up the "B" part of a tune by substituting a major 7th chord two steps down at the end of the tune (Em/D/Cmaj7/D) but some people like to keep it plain. This advice to add a major 7th was given to me by another guitarist at our session, but I leave that job up to him.