First tings first - I needed to get my hands on some wire that is stiff enough to use for the frame, and preferably not copper since the tin spreads out so much on it when soldering and there's quite a difference in color between the tin and copper. I need all the help I can get to make it as pretty-looking as possible. ;-)
So I found a 100 meter roll of 1mm (AWG 18) steel wire in a local shop and it is easy enough to make nice bends with it using pliers, and it turned out to be almost as easy to solder it as copper wires. Nice!
When unrolling and cutting pieces of the wire that are all bent and crooked so I did a quick search on the net of how to straighten wires in an easy way. Apparently one can just hold onto one end with some pliers and then use a drill to twist the other end slowly. The wire then magically ends up straight as an arrow!