Hi,
Just want to tell you the outcome, thanks for the offers/ideas in the last 2 messages.
My teacher offered to help me look in a shop, and I have found and fallen in love with a Sandberg (CA tt 4 FL). It's not wood look, but...
It's body is black (my english is not really good enough here, but I will try), but without lacquer on top, like you do with typically brown stuff to outdoor furniture, so you still can see the wood under it. And it has been sanddusted before paint so there is contours in the wood. The plastic under the strings is black, instead of white like the black Fenders, which helps towards a calm relaxed look.
It has a rosewood fretboard, with markings only on the side, really beautiful with that long piece of beautiful wood without stripes.
It has 2 singlecoil pickups like a Fender Jazz in an active/passive setup.
It sounds beautiful, very nice sustain and beautiful vibrato.
I played it already too man hours yesterday, so my left hand needs a rest today - not really what I want<sigh>
Thanks for all your valuable inputs to my decision.