If you use the 18-200 on a D600 you will get better pictures even though you are not using the full sensor. At 10MP that is much larger than the D40's 6MP, plus the camera has much better dynamic range, focusing, etc, etc etc...
So, if your budget does not permit replacing the 18-200 with an FX lens at this time, use it and you will still have significantly upgraded you capability to capture better images. (By-the-way, the FX equivalent to your 18-200 is the Nikon 28-300 f/3.5-5.6 VR, if you are looking for a direct replacement.)
It sound as if you would like a zoom with decent range for your D600. I don't recommend a fixed focal length lens as a substitute. You'll probably just get frustrated. But take one of your existing zooms, set it to 50mm, be sure to leave it there, and shoot for a day just like that. If it works for you, great, if not, you know and it cost you nothing but some time.
A fixed focal length lens should, to me, be an additional lens that you could add later to supplement your capabilities.