Actually, the best way is to use credit card. However, there are some places that would rather ask for wire transfers and pay the balance in cash when you get there. Since this is your first time to travel with your child, I suggest that you look for an apartment that accepts credit card for convenience. You might encounter problems when you get there and they don't accept credit cards. Definitely, you wouldn't want to spoil your first vacation with your child.

Any credit card of Visa or MasterCard are accepted in Europe. You may also want to consider prepaid credit cards that are ready with the chips system.

There are actually two Amex Blue Sky credit cards available. One is the Blue Sky credit card offering unlimited travel choices and no annual fee. The other is New Blue Sky Preferred that gives ultimate travel with twice the points. Points are earned from all eligible purchases.

One reason of having a credit card is the airline miles being offered with it. When it concerns airlines miles the two criteria is if it is unique with specific airline or those that can be used with any airline companies. Among the credit cards that offer the best airline miles are:
Citi Gold/AAdvantage World MasterCard
Delta Airline-Gold Delta Skymiles Credit Card
Delta Reserve Credit Card
Platinum Delta Skymiles Credit Card
Virgin Atlantic American Express Card
Alaska Airline Credit Card

AMEX is accepted in hotels and shops at the tourist areas. However, Visa or MasterCard is preferred in other places. I understand the microchips thing is not a concern anymore. http://www.creditcardshelplines.com/