Welcome, you have picked up what I consider one of the most rewarding sports. You have also opened up a huge can of worms on this site
. St Croix builds a good rod from what I read, personally I like my Redington 8'6 5wt Classic Trout as it fishes well and was very cost effective. TFO also makes solid rods for the money, but if you go with a TFO invest in a tube for your rod as they do not feel the need to provide one as other companies do. Almost any 5wt rod should be what your looking for for trout.
As far as lines go, people have a vast array of opinions but, for my .02, you can not go wrong with scientific anglers or rio. Both produce top quality lines that will last a few seasons.
Waders are also very important, breathable is what your going to want. Spend good money for quality waders as you will be whering them most of the day. Nothing short of snapping your rod is worse then have leaky/flooding waders, it will ruin anyones day. I have some LL Bean waders that do me well.
For regular 10"-15" trout you don't need a reel with drag to stop a horse, but some would be nice if you don't want to palm your reel every time you hook up. My best friends day let me borrow his Pfluger Medalist and it was fine for a day fishing WI trout. I like my orvis large arbor mostly because I got it on sale but Redington, Orvis, G Loomis, and even Bass Pro make decent reels that work great for trout.
For flies the best thing that you can do is talk to local fly shops and fly fisherman to see what works best for the streams you fish.
Your class should teach you a lot, but I encourage you to ask any questions that you can think of as there are lots of people that will answer, especially here.
other then that it is a pleasure to have met you