Check around at your local fly shops - see if one offers informal tying classes (like the Tie One On Tuesdays or Bugs and Brews), and go check it out. Once you have the basic skills down, you can tie pretty much anything. Pick a couple of flies, get the necessary materials, and tie up a few dozen of each (Elk Hair Caddis, Hare's Ear nymph, clousers etc). Expand from there...pretty soon you'll be "saving money by tying your own flies"
If you fish streamers, start with those. If you fish saltwater, even better.
I am a fairly new tier myself. I have flyfished for roughly 20 years and never really tied anything outside of the basics (elk hair caddis, woolly buggers, etc.). Trout bugs are tough, especially small stuff. What got me into tying is saltwater fishing. You can really get creative on a bigger scale, using funky colors and materials while still learning the basics. For me, tying some bigger stuff was what really what turned me around on tying.
Have fun and be careful! It can quickly devolve into a whole new hobby to obsess over....
I would forget about the kit, there are some good not to expensive vises out there, get one of those! Buy the standard TMC ceramic bobbin holder, it's the best cheapest high end bobbin holder, learn to suck the thread through! Buy the small Fiskars scissors & make a bodkin by putting a sewing needle into something! Buy veevus thread, it's strong! If you live near flyshop's & they have half price bargain bins? Then you are lucky, i love the bargain bins!
YouTube has numerous videos that help in many aspects of tying. Watch the tier closely because sometimes it is just a matter of watching for techniques which are sometimes not mentioned. Check the classified section and you will sometimes find used vises, materials, and tools. The suggestion of a mentor is a great one.