An easy pattern that works well right now is the Yellow Palmer. I caught several fish the last two hours before dark yesterday with a size 14. I don't know if I would say it is "general purpose" for the park, but when the little yellow stoneflies are hitting the water it will do the trick.
It consists of a mix of grizzly and brown hackle fibers for the tail, yellow dubbing for the body, and grizzly and brown hackle palmered forward to just behind the hook eye. Whip finish and you are done! That's right NO WINGS!! 8-)
I have my personal favorites as far as "general purpose" patterns go, but they require a little more effort than the yellow palmer. For dries the Elk Hair Caddis in a variety of sizes and colors is a good one and relatively simple to tie. For nymphs the Hare's Ear is not too tough. Then there's always the basic Woolly Bugger in case the water is a little high!
I don't know your level of experience as far as tying goes, but if you want a good start I would suggest a beginner class at LRO. I have taken just about every tying class they offer and I think they do the best job around.
There is nothing like catching a fish on one of your own creations. Good Luck!