Are you sure about this? I've flown from the UK to the Republic twice in the last couple of years and have had to clear customs both times. The reason is that Ireland is Schengen while the UK is not. However, this does not hold true if you fly from the UK to Northern Ireland as it is considered a domestic flight.

Back to the OP, I stongly concur that EasyJet is by far superior to Rynair. At the same time, EasyJet left me in a lurch this summer (irronically on a flight to Ireland), forcing me to shell out for for a last minute ticket on Rynair or wait a couple of days for the next EasyJet flight.

All things considered, I would concur with Showbizguru and book on one of the primary carriers such as Air Lingus, BMI or BA. Most offer steeply discounted "no-frills" tickets to compete with the LCCs. However, because of the breadth of their network, they are much less likely to leave you hanging high and dry in the event that things go wrong.