i find the NIB package very good for e-banking. Can see all of my accounts including VISA/Mastercard. Can make interaccount transfers seemlessly real-time. Can make payments internationally (in the case of EUR its the same cost as making a transfer to another Irish Bank). Bill payments easy enough to set up. Can do the standing orders yourself online.
On the costs side, it depends what package you go for, there are some freebank, and some with small quarterly charges (but they will pay credit interest on current acc, credit card rate 9%, have free travel insurance, etc.)