Rubbertoe..Is it solely internet banking or do you need to visit a branch at all? Do you need lev or euro accounts? Do you need sole or joint accounts? Do you need savings account as well?
For example, Bulbank's online system is great, we have a joint account with them. but we don't have a branch anywhere near us. Same with First Investment (although we do have a branch currently being built nearby) and we have a euro account with them which incurs high charges, if we want to transfer money to lev accounts. Co-Op bank is great for online current account but we can't access our savings accounts with them online. Out of these banks Bulbank is the only one that charges us a monthly fee for online access.
Additionally, for First Investment we have to use a card reader for online access whereas we don't for Bulbank and Co-Op. However, with Co-Op I have to have a certificate on the device I am accessing it from, which makes it awkward when travelling without my laptop and having to use other sytems
Doesn't help you a lot I'm afraid but put together a list of your requirements and email as many banks as you can to get details of what they can offer you.