A 10' 7wt rod is ideal. Any 7wt rod will work. If you are not going to Salmon River, then a 6wt will get you by. I would not recommend a 6 on the SR but it can be done. 8 wts are fine also but are overkill.
For a leader, I'd make it 3 sections, something like 17#, 12# 8#. You can use amnesia for butt section if you want and you'll be nymphing a lot. Amnesia to 15# to 12# to 8#. If flows are low maybe go down to 6#. I use maxima chameleon for butt section and maxima ultragreen for 12# and lighter.
For Flies, egg patterns and generic nymphs from size 10 down to 14 are fine. Fly selection or color really doesn't matter much in my experience. I'd recommend bead head everything and weighted nymphs. If you tie, I'd wrap some lead around the hook prior to tying egg patterns. When I fished egg patterns I did that. Maybe have some streamers or wooly buggers but this time of year i have found it next to impossible to get enough room to swing streamers at many of the popular spots.
Droppers are illegal in NY on GL tribs.
The most important thing when fishing the SR is to get to your spot prior to 5:00am and wait in the dark until you are allowed to fish. Getting there at 5:00 gives you probably an 80% chance to hold the spot you want. If you are catching fish, by 8:30 you'll be surrounded by Russians if you're not in a fly zone and you'll be crowded out. If you fish a fly zone, especially the lower one you might need to get there a bit earlier. You won't get crowded out by russians, but you will get crowded out by some of the many "Salmon River Pros". The good news is that these pros will be sharing all sorts of "pro tips". If you pay attention to these "tips" you'll have a great sense of what not to do LOL.
I know I'm being negative, but if its your first time you'll have fun and catch some fish.