Be cautious with banks having crazy transaction fees for generic stock. Most of them have own funds and you can purchase them for low fees, while the rest can be even at 15 EUR per single transaction.
Depending on what European country you are in you could also have a look at brokers/online banks, these usually have more sane fees.
In central Europe flatex would be an example of such a broker. Though I am not sure in which countries these are available.