As I see it, it depends on what kind of “rembetika” you have in mind.
There is a type of rebetika played on a solo guitar as those by Katsaros. You must look him up and listen how he plays. This will answer to most of your questions.
There is also a type played with one or two “baglama” as in “Giorgos Batis”. There is a small space for guitar in his songs though.
On the other hand we have the widely known “company” based rembetika. In this case you play with a nylon string guitar that gives a bass sound needed to accompany the high tremble of the bouzouki and baglama.
In Athens there is Nikos Mbras (Zoodochou Pigis & Valtetsiou corner - Exarcheia) who might build you a rembetiko guitar if you come to an agreement.
Must warn you though that I’m not a guitar player. I play bouzouki and all I can do is to judge when guitar is good and played properly.
You should always keep in mind that there are no real standards in this kind of music. And that is a reason that it is still alive and kicking!