Any kind of wire that won't be pulled out of shape by the hanging objects. I usually use old coathangers for the top bit, but you could use all sorts of other stuff as well--someone on here recently suggested using a bike tire rim for the top of a mobile, and there's a REALLY COOL mobile here http://www.craftster.org/forum/index.php?topic=171997.0
made with a melted record. Old lampshade harps and frames work really well too. The biggest problem I have is arranging all the bits and pieces so they hang evenly without tipping the mobile. I'm sure there's a better way to do it, but I just use trial and error until it hangs right.
Other tools possibly needed:
Thin string or fishing line-- to hang your mobile items with
ruler -- to center the string, so your cards will hang straight
Needlenose pliers--to bend wire and close crimps
fishing weights or jewelry crimps (optional)--if you clamp one of these onto the string just below an item, it will help keep the item from sliding and will add a little weight to help keep things from tangling up.
Small beads, buttons, trinkets, or washers (optional)-- add color and interest, can also be tied onto the string to keep other items from moving and to weight the mobile.
Some way to attach the postcards. If these are postcards you want to preserve for later use, it's probably not a good idea to string them by gluing, taping, or punching holes in the card-- you might want to make a very lightweight frame (cardboard, balsa wood, etc) and attach the string to the frame instead of directly to the card.
Good luck with the mobile! It sounds like a cool idea.