things have gotten better over the years since I began. Look for a fly specific kit. Meaning one that has a list of flies you can tie with it from start to finish with the materials provided. Not a cheap kit that has a bunch of 'stuff' that you can't really tie anything with. don't buy a cheap kit! Or you'll end up replacing most of the tools and the materials you'll throw away! Or buy one that has quality tools as I posted below, you'll still need materials to finish it out.
Most kits suffer from poor quality tools and just the same poor quality materials. Lower end scissors, bobbins, vises. They work but you'll likely end up replacing some or all of them depending on how into it you get. If I sound like I'm repeating myself I am for a reason! To many of us were suckered into buying junk. I still 20+ years later have some of that junk. I use the cheapo scissors for cutting wire when I'm too lazy to helicopter it off lol. The rest I threw in the trash!
Learn the process's than move on to a new bug. Start simple, say a illiamna pinky (chenille egg pattern 1 material fly), to a salcha pink (same egg pattern with a turn or two of white hackle up front) to say a bead head thread zebra midge for fly another 2 step fly. Griffiths for fly 4 which will teach you to palmer hackle, something you already had a taste of with the salcha pink. From the Griffiths you can add a tail and make a wooly bugger on a bigger hook. Than jump to the PT. Base your flies using one to build to another fly with another step, learning the process and proportions. Eventually you'll pick a fly and just tie it. Use the right materials and think about proportions. Don't worry about size right out of the gate, tie a little bigger...panfish don't care! And stop before you think you need to, IE DONT crowd the eye LOL!
Here's an ok kit. nothing fancy and it wont break the bank.
http://www.fishusa.com/Product/Wapsi-Deluxe-Fly-Tying-Starter-Kit
A little nicer kit with a dvd
http://www.jannsnetcraft.com/fly-tying-kits/620806.aspx
Even better tools kit but you'll need more materials which is an easy find (cabelas has the jack dennis beginners kit (no tools) with dvd for another 89 bucks. You likely wont be upgrading the tools in this kit very soon. The vise is a better low end vise with a giant range of hook holding capacity!
http://www.schmidtoutfitters.com/index.cfm?fuseaction=product.display&Product_ID=983
For learning to tie youtube is your friend these days! Heaven forbid we buy books LOL! Honestly its pretty dang awesome watching the greats bust out flies....it really is a great thing! Its just too easy to see someone tie flies vs read, but lord knows I have an overflowing library.
You tube these guys, Davie Mcphail, Hans Weilemann, tightlinevideo, Johnny Utah, intheriffle and a pile of other great tiers on youtube right now. It's a great time to learn to be a fly tier! I believe one of them are on this site as well (intheriffle? and johnny Utah?) cant remember which one they were!
This one should be in All PA' guys library. https://www.youtube.com/watch?v=ngSraA6whFM
https://www.youtube.com/watch?v=fWoGLzyyzdc
If you have a shop nearby, stop in and see what they carry. Some places make fly specific packages. Look at the make of tools. Are they quality scissors that fit your hands? Ceramic bobbin with a lifetime warranty? Does it come with a half hitch tool or matarelli whip finisher. Word of advice, buy the whip finisher but find someone who knows how to use it. They are FAST and good! But can be frustrating at first. I like the full rotary some guys prefer to turn them by hand or do a full whip by hand.