Not of lot written about actual armour and equipment, but reading the invasion of Stringbow and Henry’s Invasion has the most documents available.
The nobles would be similar to the mainland nobles except seem to have fought on foot predominantly with the professional hearthguard (Curaidh) although some armies seem to have mounted units of knights but very small.
Depending upon the kingdom, the foot were broken into freemen heavy foot (Bonnachts and could include the northern gallóglaigh axemen) spear, plus a lot of poorly armed and majority of unarmored levy Kern armed with javelin or sling, and small component of archers and some crossbow in the city garrisons.
Some good books on the subject
Duffy, Sean. Medieval Ireland An Encyclopedia.
Martin, Francis Xavier (2008). Volume II: Medieval Ireland 1169–1534. Oxford University Press.
Bartlett, Thomas (2010). Ireland: A History. Cambridge: Cambridge University Press. ISBN 978-0-521-19720-5.
Flanagan, Marie Therese (1989). Irish Society, Anglo-Norman Settlers, Angevin Kingship. Oxford: Oxford University Press. ISBN 978-0-198-22154-8.
Flanagan, Marie Therese (2005). "Anglo-Norman Invasion". In Duffy, S (ed.). Medieval Ireland: An Encyclopedia. New York: Routledge. pp. 17–19. ISBN 0-415-94052-4.
Gillingham, J (2000). The English in the Twelfth Century: Imperialism, National Identity, and Political Values. The Boydell Press. ISBN 0-85115-732-7.
Good website for trawling through
https://celt.ucc.ie/published/T100005C/Cheers
Matt