In Amsterdam NL a backend engineer could expect 80-100 euros/hr. > 100 is also possible, but you may get into specialization territory.
By the way, I am not totally convinced about weekly vs hourly billing. In my case, hourly billing has worked well. I just make sure I bill for _everything_ I do for the client, also the time I spend learning stuff, and communicate clearly about it. People hire me because I can figure out stuff quickly, not because I know all there is to know about programming (though I do think I have a strong background).
Once you have a few 6 month contracts under your belt and you can get good references you can probably find things without relying on intermediaries.
In my experience no advertises on job boards that they are looking for contractors.