On a 12,000 mile 4Wheel tour of the West with German friends, I put the 20 on my camera and just forgot I had any other lenses aboard the vehicle. Took the extra batteries and cards out of the camera bag, zippered them in my jacket pocket, and didn't open the camera bag again until we were back home. Nothing beat the 20 for scenery, and the depth of focus meant you barely had to focus it. Sharp as a tack and fast. My recipe for a trip: lightest, smallest body you can find and the 20mm lens!
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Congrats on the new member to your collection. I also buy only (when I can) full frame lenses. They work fine on Nikon DX cameras and will take advantage of the full frame also. Having both a DX and FX camera (I have a D70s (my wife's) a D7100, and a D610) I love carrying both the D7100 with a long lens or long zoom and the D610 with a short zoom or 50mm. It keeps me from having to stop and change lenses and miss a shot. It also gives the additional reach with the DX camera without having to change the FX to DX mode and forgetting to change back. But, having all of my lenses compatible makes it easy when in the field to pick 2 general lenses that cover the length. (for instance, 28-300 on the D610 and 80-400 on the D7100). This gives me a coverage of roughly 28mm to 600mm with no gaps and my ISO is generally good enough on both cameras for any shot. Sure the D610 weighs more than the D7100 and the 80-400mm lens is anything but light, but I have a Blackrapid dual camera strap and it is easy to grab the appropriate camera for the shot.