IMHO I would not get a complete kit. Vise, tools ,feathers ,fur etc .. A good way to start is to take a local FT course at a TU chapter or flyshop. I think a vise is the most important part of the setup so ck out this site:
Fly Tying Vises In-Depth Review by Fly Fish Ohio!
as for tools you need:
- a good sharp pair of scissors $5-$25
- a decent bobbin $5-$25
- A dubbing needle ,, make your own with a sewing needle & a swizzle stick.
- Decent pair of tweezers $2-$10
- A whip finisher, or better yet learn to tie off a fly by hand. you'll thank me later..
If your not going to take lessons, get a instructional video. It's important because there are a lot of little tricks & procedures, Hand position & such, that books can't show & they will make it a lot easier to start & will avoid your getting frustrated & giving up.
As for materials, decide what you want to tie. a lot of beginners start out on Wooly Buggers because they're fairly large, easy to tie, use most of the hand & attachment techniques & most of all they're a great all species fish catching fly. You don't need many materials: hooks, chenille, marabou, some type of hackle feather, thread & perseverance.
Like I said, I feel that a good solid vise is very important. There is nothing more frustrating than having the hook slip in the vise while your tying something on & watching the fly loosen up or unravel. I'm sure I left something out soooo....I'm relying on the other posters to chime in...