Unlike some other countries, there is only one sort of mailbox here. Which means you will have no problems whatsoever choosing the right mailbox to put your letters/ cards in. The mailbox is yellow and will transport all your cards, even - in most cases - those without stamps. In that case the recipient has to pay to receive your card/ letter. I wouldn't take the chance of lost mail and rather put a stamp onto whatever it is.

However, Germany is a little funny about the size of the card/ envelope. The even greater problem ist that many postcards, or souvenir cards that come with envelopes, are just a trifle too big for the normal price of a letter or post card. I find this rather unfair, because you can hardly see the difference. To be on the safe side, instead of choosing the big flashy postcard take the smaller one, and instead of sending the slightly bigger birthday card, choose the smaller sized one.

Then you pay:
 for a postcard to anywhere in the world by Air Mail: 1.00 Euro, within Europe: 0.45 Euro
 for a letter (20g: envelope plus around 3-4 paper sheets inside) to any place in the world by Air Mail: 1.55 Euro, within Europe: 0.55 Euro
 Aerogramm, these thin blue things you're always scared to tear apart, to anywhere in the world by Air Mail: 1.00 Euro

And if your not quite sure, go to the post office, for example to the one inside the Hyatt Gallery (Mönckebergstrasse) or Central Train Station and ask. Or just take a chance, it works most of the time. Postmen don't seem to have tape measures in their pockets every day.