Everyone nailed it so far. I would look for a cheap vice first though in case you realize its not for you. here is a list of things I would suggest you get.
vice-
start cheap order a cheap Thompson or something from ebay, or see if someone can lend you one, or give you one. I just gave mine away or I would hook you up. I am sure someone on here may have a beginner vice for you.
-If you are set on doing this, and feel you would really like tying, I would suggest a regal or renzetti traveler. Buy one vice and have it for ever, or just get replacement parts. Regal is my brand that I would go with to be honest. Great guys to deal with, and a great quality vice
Tools:
-good pair of scissors!!!-vitally important
-3-4 bobbins- annoying to only have one and switch thread
-whip finisher- not impearative but I enjoy this tool
-small hackle pliers-will pay off big when working with hackle on dry flies, especially small ones
Thread:
get a few spools of 140 denier or some smaller /0 threads
-olive, tan, black, white, brown
-these smaller diameter threads will help with not bulking up the fly a lot, and cause you less headaches. I like the 140 because it is a bit more durable, but can cause some issues with fraying.
-get a few in chartreuse, orange, and pink for hot spots
Hooks and hardware:
-a few packs of 7/64th, 1/8" beads (gold, black, and copper)
-pick up a few packs off hooks in wet fly or nymph in standard or 1xl variety
-size (18-12)
-a few pack of shrimp/caddis hooks size 16-10. I will tie some eggs on these hooks as well, work for midges as well
Materials: (If I forgot any please chime in guys)
Decide on what flies you want to try and tie. The following would be good for some go too nymphs for pa.
-Pheasant tail, hares ear, copper john, prince, walts worm, Muskrat, midges, green weenie, san juan worm, caddis patterns
-hares mask or hares dubbing in (natural, olive, black)
-pheasant tail clump-(natural, black, yellow are my favorites)
-peacock hearl- in strung or tails. I like the strung for most of my patterns
-brass wire (get this in a few colors and sizes I like the brassie, and small sizes my self
-flash back material- great for adding some flash back wing cases
-Turkey tail feathers, great for wing cases
-Goose biots (white, black, and brown)
-medium chenille-chartreuse, FL pink
-Hungarian patridge soft hackle-adding wetflies, and soft hackles to the mix
Dries: These materials should get you, Hendrickson, Redquill BWO, Adams, Sulfur, Elk hair caddis, some wulff patterns
Body:
-Look into the superfine dubbing box to start out, a few different colors of dubbing to make generic dries
-quills- easy to work with, I like the pre made quils myself but you can remove the fibers from hackle for the same thing, but not worth it IMO
hackle:
grizzly, brown, ginger, and grey dun I would suggest looking into the smaller packs in predetermined sizes to start out with. No sense spending 100's of dollars on necks
wing material:
-elk hair pick this up in natural and black for caddis patters
-calf tail- not impearative but works on some classic flies
-mallard flank, get this in white and yellow colors
others:
foam- great for crickets, hoppers, ants and other terrestrials
Tips:
-I would stay away from the beginner kits, often times your are given material you will never use, and less quality at that
-stick with it, it takes a long time to get the hang of things, and you will be constantly learning
-find a mentor- a huge amount of the learning curve can be cut by finding a mentor or joining a class
-youtube is your friend-there are a lot of videos out there, and posted on here for you to follow, Site Sponsor Allen Fly Fishing has quite a few on there page
-Don't give up- this aspect of our sport is addicting and catching a fish on a fly you tied yourself is like nothing else.
-Don't be afraid to try new patterns- very fun to grow your skills
-Learn proper proportions for flies, This is not a deal breaker when catching fish, but will make your flies look more uniform, and better. I was guilty of this, but got some constructive criticism on here and took it to heart. my flies look a lot better.
-Don't be afraid to ask for advice- many guys on here to help you out, and learn from
-GOOD LUCK, this is addicting and very rewarding.