Vertical Jigging is a technique based on feel, so you’ll want to start with a very sensitive rod. I consider river walleyes as “samplers”. As things drift by they suck them in their mouths, sample them and then either eat it or spit it. A bite happens very quickly and you have to react quickly to get a hookset. That said, I would choose at least an IM-8 rod (45 million modulus), the more modulus the lighter the rod and the more sensitive the blank. Combine that with a small, lightweight reel (something rated as light or even ultra-light). Lastly I recommend no stretch FireLine in 6-2 (6 pound test, 2 lb diameter). Because it is a no stretch line, you will have much greater sensitivity, but the no stretch will also make it a little harder to fight in the fish without tearing the jig out of its mouth. For that reason I use a Medium Light action rod. If you want to use mono (say Trilene XL in 6 pound test), then I’d go with a medium action. The medium action rod will compensate for the line stretch on the hooksets.
In the Walleye Angler Signature Series of rods from Bass Pro Shops, the WA60MLJS rod is a 6 foot medium light action IM-8 model. The model WA60MS is a medium action IM-8 rod for the same price ($89.99). Add on a Bass Pro Shops Pro Qualifier reel (model PQ10) to either rod and you have a great river jigging combo.