If you want plenty of feisty brookies, try Cosby Creek. It is tucked in one of the quieter areas of the park and you don't have to hike for miles to catch some decent sized brook trout (6 or 7 inches being decent sized).
Another stream not far from there is the Middle Prong of the Little Pigeon aka Greebriar. One of the larger brook trout I have ever caught in the park came from a plunge pool just downstream of the Ramsay Cascade trailhead.
Walker Camp Prong is another good stream for brookies with easy access, but it is shadowed by US441 so you may have to deal with a lot of onlookers.
As far as flies, my personal favs are either a size 16 THunderhead or a 16 TN Wulff for the broookies. As long as you are stealthy and present the fly well, they will usually hit it.
As for snakes, never have seen anything poisonous while fishing. Just use common sense on where you place your hands when climbing over boulders, and look on the other side of logs before stepping over them. I have had to worry about stinging insects more than snake for the past few years!
PM me if you want some specific locations and directions>