Ulster bank have a very good start-up deal for businesses. Can't remember full details as it was a while ago I was looking at it, but as far as I can remember there was no free overdraft facility. Worth looking into.
Bank of ireland also do a fairly good package I think.
But, you should NOT use your regular current account for your business activities. You should set up a business account seperate to your own. It will be easier for you, your accountant and The Revenue.
I use Bank of Scotland, happy with it. Free banking (I believe the only one to do this but open to contradictions) plus it gives interest under certain conditions. Very straightforward to get set up. No free overdraft, but from the comments maybe none of the banks do this.