Nothing is free. Bank accounts in the UK have mostly been "no fee", but then they charge huge amounts for other things (and now there is talk of the banks there starting to charge). I would look at the full range of services you use them for and make a decision on a higher level than focusing just on the credit/debit card fee. Most banks offer you discounts if you use several of their services.
As mentioned, S-pankki is free. The Nordea-Stockmann card is also free though you need to pay monthly fee for Nordea to have online banking codes, unless you're sufficiently young (less than 30 or so) or "good enough" customer (such as having a big lone from them), in the latter case you can also get other cards from Nordea free as well.
Several other banks also I think give free basic services to young adults, and also many wave fees from the "good enough" customers.
AFAIK Handelsbanken doesn't charge any extra fees for your normal daily banking, including online access, nor do they have any "key customer" schemes. I have a Visa, which has an annual fee (don't know about Visa Electron), and there's a limit a free-of-charge cash withdrawals in a month, but other than that I'm not paying for anything else and I don't have savings or loans with them.
Käyttötilin korko Käyttötilin hyvityskorko on sidottu Handelsbanken Prime -viitekorkoon vähennettynä 3,0 prosenttiyksikön marginaalilla. Korko ei voi alittaa 0 prosenttia. Korko lasketaan kuukauden alimmalle saldolle
There isn't a bank that would currently pay any interest to an account you can use pay daily expenses. OK, S-pankki would currently pay one euro per year (0.1%), and Tapiola three euros (0.3%), if you had an average balance of 1000 euros on your account for a year, but most people wouldn't care, or if they did, then they shouldn't keep that 1000 euros on either of those accounts either, when one could keep the balance close to zero, and pay with a credit card (without annual fee, paying that bill always in full) and have that money somewhere that pays at least slightly better interest than 0.3%.