As the others have mentioned, the easiest and usually least expensive way to get local currency is to use ATM's in each country. While each bank may charge fees for use of the cards in other countries, the exchange rate is usually charged at the "interbank rate" which is usually the most favourable. Note that ATM's have different names in various countries. For example, in Italy, "Bancomat" is the term, in Germany you'll probably find them labelled as "Geldautomaten", while in the U.K. "Cashpoint" seems to be common.
There's often a debate here on the Forum regarding whether or not to travel with cash. My preference is to have 50-100 in the local currency to cover incidentals like meals, taxi fares or whatever until I get settled in my first location and can find an ATM. There are always ATM's at airports, but I'm usually in a hurry to get out of there so prefer not to stop. I usually have money left over from previous trips, so that's what I use to cover travel expenses on the next trip.
I would highly recommend packing along a "backup" ATM card, in case of a problem with the primary card (I've had that happen). Also, be sure to notify each of your banks and credit card firms that you'll be travelling, so they don't "freeze" your cards when they detect transaction activity in Europe. I don't have any suggestions to offer on the "best" ATM card to get, as the products here are different than those in the U.S.