Re: Need help choosing the right rod.
Welcome to the board. You've gotten great advice from Dorian and Larry. Where abouts do you live, and what are the fly fishing opportunities close to home--- it might help zero in on an another outfit looking beyond your trip to the Green, but also being geared for that too.
Although your 8 weight will "work" it's much more suited to bass, steelhead and light saltwater for everything from stripers, bluefish, redfish, sea trout, bonefish-- and is a great choice for those fish.
You may want to give some thought into where you'll go from here in terms of fly fishing-- looking beyond your trip to the Green a bit to other opportunities around you more locally. It's not uncommon for folks to have several different rod weights for different types of fishing. For fishing different conditions/species it might be a good strategy to skip a couple of weights in terms of bang for the buck-- 8-6-4 or 8-5.
Since you have the 8 already, you might want to consider a 5 weight-- it's a great all around trout weight-- a little more oomph than a 4 weight in windy conditions, but still delicate enough for fishing small dry flies. It'll let you throw larger dries like grass hoppers and stimulators on other rivers, as well, and of course not too much of a difference between a 4 which is a bit more suited for delicate presentations, shorter casts and small flies on spring creeks or specialized tail waters like the Green and 6 which is more suited for throwing bigger stuff (streamers, heavily weighted nymph rigs, large dries and longer casts on bigger water like big western rivers in windy conditions.
A 5 and 8 is a great combination for all around fly fishing in FW and light SW and might be the most versatile combination you could get in just 2 weights worth of outfits.
If you end up "specializing" in rivers like the Green where small flies are the rule, fishing for panfish or small streams for small trout etc you could add a 3 weight down the road, (but that is a lot more limited in terms of fishing for other stuff.), and at that point you'd end up with an 8-5-3.