You've gotten great advice about taking a class. A lot of fly shops and local fishing groups should be offering them thru the winter months. You'll learn a ton, and get a chance to ask a bazillion questions, and get to see and use different materials and tools. And you'll learn a bunch of tips and tricks that will save you years in the learning curve and a lot of frustration. Classes are also designed to build on easy patterns to teach a variety of techniques, so in the course of a typical 6 week course you may have learned 12 patterns, but each pattern is typically a "style" of fly, that you can modify with size and color to tie a whole bunch of stuff once you've mastered the technique of tying that style.
You might even be able to arrange to use a borrowed vise and tools for the first few classes, while you shop around for a vise familiarize yourself with different features (base vs clamp, fixed head vs 360 rotary vs "true rotary") and the different brands and prices to find one that works for you.
Here's a search link for Trout Unlimited chapters. Hopefully there's one near you:
Council/Chapter Search | Trout Unlimited - Conserving coldwater fisheries
Like others have said the kits sound like a good idea because you get a bunch of different materials and a basic tool set for a great price. But in most cases you'll get a 9 dollar vise with soft metal jaws that won't hold hooks very well and poorly machined parts, a bunch of odds and ends for materials and probably a lot of stuff you don't need and not enough of the stuff you do. If you stick with tying you'll probably want to upgrade the vise and many of the tools very soon. A kit might be the way to go if you have a limited budget of 50 bucks or so, or are unsure if you'd like to tie and want to just try it.
IMHO, if you think tying is something you really want to do, you're much better off going into a local fly shop from folks that actually tie and having them set you up as opposed to buying stuff online from a big box store. They should be able to put a rocking set up together with a budget of 150-250 bucks.
A good vise will run from 75-150 or so. Here's a great review of different models:
Selecting the best fly-tying vise, by Hans Weilenmann and Bruce Salzburg
Good quality tools about 30-50 would include;
Bobbin- metal tube Griffin for 7 or ceramic tube bobbins by Griffin, Dr Slick, Tiemco, Wasatch, Materelli, Rite etc 13-20 (Ceramic tubes won't cut through thread as easily as metal tubes)
Bodkin- just a needle on a stick, any import will do 2 bucks
Scissors Dr Slick or Anvil 13
Whip Finisher Materelli 15 or "Materelli style" import 7
Dr. Slick makes a tool kit that includes the above (with ceramic tube bobbin), plus a bobbin threader, and a hair stacker for about 39 bucks and is a good quality tool set.
Materials for 2 easy to tie patterns that will also build up your inventory of basic materials good for your waters that you'll be using a lot on other patterns for a long time 20-30 plus cost of hooks. Buying materials for 1-2 patterns (maybe in a few different colors too) is a good way to go, instead of trying to buy everything at once. That way you'll make sure to get the stuff you need and won't get overwhelmed trying to figure out what stuff goes with what pattern, and you can gradually build up your inventory as you learn.
Hope this helps.