I would head down to your local fly shop (in your case Tailwaters would be a great place to check out). Ask them what they recommend, I would pick out a few woolly buggers which will work well for both bass and trout, a couple of poppers which are great bass flies, and a few nymphs and dry flies to go after trout (pat's rubber legs, san juan worm, egg, and copper john are my four go to trout flies).
A lot of fly shops have plastic containers they will give you for free to hold your flies. Or you can invest in a fly box that keeps them separated. I have several fly boxes, one for bass, one for trout, one for carp, one for saltwater, but that has more to do with my OCD than with really being essential.
A five weight rod, reel, line, and some tippet is all that is really essential. It doesn't have to be expensive to get you out there fishing and catching a few. Echo is a great company
makes a great starter kit which has everything you need. Everything you buy after that is about convenience and comfort.