A Touch of Midas
about a half-dozen of the fly patterns you most commonly fish with. Write down your list of flies, then look up the patterns or "dressings" in a fly tying book to see what material you need to purchase.
Start with an inexpensive vise and tools; if you really get hooked by this hobby you can upgrade your tools later. Many experienced fly tiers have taken the Swiss watch approach to the tools they use - they buy high quality instruments just for the pleasure of working with them. This is not necessary, however. I have a simple but sturdy vise I bought 30 years ago and it works just as well today as it did then. I still use it on some occasions to hold small (#18 - #22) hooks.
Other tools you must have include a hackle plier, a bobbin and bobbin threader, a bodkin or needle, a hair stacker, scissors and a whip finisher. You may want two pair of scissors, one to cut heavy things like copper wire, tinsel and deer hair, the other to cut thread and other fine items. A whip finish is the final knot used when a fly is completed; you can learn to tie this by hand, but a tool makes it quick and easy.
Later you may want to add a dubbing twister, another bobbin or two and a hackle gauge. You may also want some kind of tool caddy to keep all this stuff in and a desk lamp to help you see what you're doing. A box of some kind to organize your hooks in is helpful. If you are fortunate you will find a permanent home for your tying material in a desk of some kind.
What flies to begin tying? Woolly Worms and Woolly Buggers are a good place to start. The Hare's Ear, Pheasant Tail and Red Squirrel nymphs are terrific flies, and any book should include a list of the materials you need for them. Good Midwestern dry flies include the Adams and Elk Hair Caddis. Chuck and Sharon Tryon, in their book Fly Fishing for Trout in Missouri, include the Hare's Ear and Squirrel nymph, but also add the freshwater shrimp (scud), yellow and grizzly Woolly Worm, Zug Bug, a dark stonefly, flies called soft hackles, the Thunder Creek streamers, and the Renegade and Griffith's Gnat, plus some others, for Missouri fishing.