That post peregrines made is likely one of the best you'll find. Bare minimum, a vise, scissors, & a bobbin. Other tools are useful as you progress, but not necessities. As has been said, you want a good pair of scissors, with loops large enough to comfortably fit your fingers, and a bobbin with the ceramic inserts. Regular bobbins with metal tubes work for awhile, but wear out quickly, so you're better off with the ceramic from the start.
I tie on a Regal vise, and like the rotary feature, but for the tying I do it's also not a necessity. I have a home made vise too, made from an old pair of Vise Grips for tying very large flies & even tie jigs with it, and it's not rotary, but works just fine. Whether or not you need "true" rotary is up to you. For me, not really needed.
Kits can be a way to start, but frankly most will agree not the best way since materials that are included are usually poor quality & you end up paying for things you may not use. IMO, best bet is to buy as you need, from a reliable supplier, for the patterns you wish you tie, and build your materials inventory as you progress. You will find that the more involved you get with tying, and different types of flies, there is a lot of overlap with materials.
Just be prepared, tying is an addiction!