I would caution you against buying a "cheap tying kit" mainly due to the fact that several of them have vises that don't, and won't, hold a hook securely in the vise jaws. And trust me, nothing is more discouraging than trying to tie on a hook that won't stay in place. Griffin makes what they call a Model 1A Fly Tying Kit that comes with a 1A Vise, Bobbin, Hair Stacker and Hackle Pliers for around $60.00. Although the vise is considered an entry level vise, it is a good quality vise and most importantly, will hold your hook in place without slipping. The 1A Vise can be purchased by itself for around $45.00. Another important item is a good sharp pair of scissors that are made for fly-tying. Dr. Slick manufactures some decent scissors. Their are probably some other good quality tools in your price range out there besides the ones above, and I'll let someone else "chime in" on those.
Also, pick out a few simple patterns (Gold Ribbed Hare's Ear Nymph comes to mind) that you think you want to tie, buy those materials only, and then see how you get along with those patterns. While their are a lot of great books and videos on fly-tying, it would be a great benefit to you if you could watch someone tie, or maybe get enrolled in a tying class.
Here's one fly-tying site that may give you some help. They have a basics section.
I kind of think you can get started for around $100.00. Be forewarned though.
Tying is just as addictive as fly-fishing, maybe more so! I'm sure that there are a lot of members here (myself included) who will help you in your new endeavor. Good luck, and I hope this helps