Also from experience, I'd say go router first.
I helped with design of the Darwin, the first in the line of RepRaps. It was a cumbersome and very fiddly device, but it got the job done. The newer Mendel is a much more elegant and stable design.
I don't yet have a router, but here is my reasoning for building a router first. Its quite simple and it goes along the lines of why the RepRap project exists. Your router can build your printer for you! Yes you will need the motion control and the electronics, but a router can easily make the parts for a CNC FDM printer.
However, a CNC FDM printer cannot make the parts for even a small sized router. The forces that nearly every CNC router is exposed to are much too great for the pile of plastic parts that would add up to be whatever sort of router you could design.
As was stated earlier, 3D printers are essentially plotters with a Z axis. If you are capable of building a square box, then you can easily fill it with a 3D printer (see the Makerbot CupCake).
The Makerbot Cupcake was designed to be cut out with a laser cutter and the plans are freely available online: CupCake CNC.
I'm sure that one would be able to alter the design to be able to cut it out with a CNC router.
Hope that this helps with the decision process.
Jay Swift
"The bitterness of poor quality remains long after the sweetness of low price is forgotten"