As others have pointed out there's a trade off between the cost and quality you get with the kits. So depending on your budget, and how sure you are that you'll get into tying, you could go the kit route-- just be aware that the vise may not be the greatest, since most kits come with soft metal jaws and are often poorly machined. Materials may also be limited. But if you're looking to limit your upfront investment to 60 bucks or so all in for vise some tools, a few different hooks and materials, then a kit is probably the only way to go. I would look for one that seems to offer the best selection of patterns you actually want to tie. Some also come with a DVD.
I can't knock kits, since many of us, including me started out that way, and money should not prevent you from tying whatever your budget. You'll likely want to upgrade the vise at some point, and you can use the experience you've built up tying to shop for a better one, especially if you run into other folks tying and get to try a few different styles of vises.
The other way to go is to put a "kit" together yourself. Depending on your budget you could get some old reliable standards that you could pass along to your grandchildren.
Old, used Thompson Model A c-clamp for about 25 bucks can sometimes be found on ebay, craigslist or "for sale" sections of FF boards etc.
I would also look for deals on used vises like these. They're excellent new of course, but are also bulletproof and might be good ones to look for if you can find a used one at significant discount off retail.
DynaKing Kingfisher or HMH Silhouette SX about 130 new
Regal InEX 120 new
Peak Rotary 140 new
Plus tools. Dr Slick makes an excellent toolkit for around 50, or you could select some "decent" ones yourself for around 30 bucks
Griffin metal tube Bobbin 7 bucks
Bodkin- any brand 2 bucks
Scissors- an inexpensive pair of 4" sewing scissors with a fine point about 4 bucks
"English Style" Hackle Pliers any import 2 bucks (if you want to tie flies with wrapped hackle like trout dry flies)
"Materelli style" import whip finisher 7 bucks (or original 17 bucks)
Hair stacker, any import (metal with two ends for stacking hair on small and medium flies) about 7 bucks if you want to tie hairwing flies like Elk Hair Caddis
From there, you'd add hooks and materials for a couple standard beginner patterns at a time. As you knock off flies, you'll also be building up an inventory of hooks and materials.
Fly tying is a lot of fun and hopefully you'll get a lot of fun out of it. There are a lot of reasons to start tying. The only caveat is that saving money is probably not one of them... The temptation is to tie a lot of different things requiring different materials, and unless you're tying a ton of flies that you'd be buying anyway, it'll end up costing some money like any other enjoyable hobby.
As far as instruction etc, you might want to do a search for a TU chapter near you (the a Hiawatha chapter in Rochester might be close to you.):
Council/Chapter Search | Trout Unlimited - Conserving coldwater fisheries
Most chapters have fly tying courses or at least informal get-togethers where you'll learn a ton, as well as group trips to local water, casting clinics or informal casting on the lawn before meetings etc. It's also a great way to see and try different gear as you run into people with different stuff.
Good luck. Keep asking questions, i know this can be pretty confusing.