Realex
does have an Internet terminal.
Also, if you go in with a decent plan for your Internet merchant account, the bank usually starts at 2.5% to get you going. Second year, depending on volume, you can negotiate your rates.
Hold on... more holes... you don't need a merchant account with your local bank if you go for WorldPay. WorldPay act as your merchant account and payment processor all in one.
Have a read of this and then maybe redo yours:
blog Guide to Selling Online | davidbehan | web design - web development - web marketing | ireland
It was written about a year and a half ago but still very accurate.