The best bet is to find a local fly shop that offers beginning tying classes and have them put together a "kit" of separate components and materials/hooks for a couple of basic patterns for the fish in your local area. If your shop doesn't offer them, they'll probably know a local club that does, or be able to arrange to teach you a few things. Some of the larger big box stores (Cabelas and Bass Pro) might run free classes too, if you don't have a local fly shop--- Giving the local fly guy business is good kharma and you'll have a resource to go to with questions etc. You'll learn a ton with a few lessons, and it'll really help your learning curve.
Most prepackaged kits come with a 9 dollar Asian import vise with soft metal jaws and poorly machined parts, and a hodgepodge of materials and about 20 hooks in various sizes for "saltwater" that may include stuff for anything from bonefish to sharks. You'll probably find you'll have a lot of stuff you don't need and not enough of the stuff you do. The vises typically don't hold hooks well, and because of the larger hooks and increased thread torque used on salt water flies, this tends to be a problem pretty fast, and you'll want to upgrade pretty soon anyway after the first few dozen flies.
A decent vise is a chunk of change, and is usually a matter of personal preference, so if you can take lessons on a loaner before plunking down money to see what features you like, that would probably be ideal. Pedestal vs c-clamp, fixed or adjustable angle, non rotary, 360 rotary, "true" (inline rotary), range of hook sizes the standard jaws will hold (and availability/price of optional jaws for different size hooks) etc are examples of stuff to consider when shopping for a decent vise, so some familiarity with tying is a good idea. Here's a link that might be helpful that also applies to saltwater
. Browse the embedded link for a review of vises to get familiar with some names and different styles. If you go this route, figure for a decent vise 80-150 bucks, tools 35-50, and some starting hooks materials 25-50 (mostly depending on quantity/sizes of hooks).
If you are on a limited budget, say 50 all in for everything, or not sure if fly tying is something you really want to do, than a kit is probably the only way to go. Try to find one that has patterns you will actually use.
If your budget is around 100 all in, rather than a kit, I would go for a Griffin 2A vise, over a cheaper import, plus some basic tools for about 80 dollars:
Anglers Workshop - Griffin 2A Vise and Tool Kit
The vise is not the best in the world, but has a lifetime guarantee and is made in the USA and will handle SW size hooks fairly well. (The vise alone usually retails for around 60 bucks). You’ll likely want to upgrade the vise and some of the tools fairly soon if you stick with tying. You can add about 20-30 bucks in materials and an additional tool like a whip finisher and bodkin to get started.
Materials for saltwater are typically inexpensive (as opposed to trout stuff with expensive dry fly hackle). A local fly shop can help pick out materials for your local water. But just to give you an idea some easy to tie patterns that are effective pretty much anywhere in SW:
Hooks: a pack of mustad 34007 (or 3407 if you can find them) will run about 5 dollars for a 25 pack or 12 bucks for a 100 pack
Bucktail: Chartreuse 4 each
Thread: Chartreuse Danvilles flat waxed nylon, or Danville or Uni 3/0 2 bucks each
Flash: Pearlescent Krystal Flash 3 bucks
Lead dumbbell eyes: 24 pack for 3 bucks
If you buy a 25 pack of hooks and a 24 pack of lead eyes you’ll have 2 dozen chart clousers, but plenty of flash, bucktail and thread left over to use on other stuff.
After you’ve whipped up some chartreuse clousers, add some additional stuff down the road to the above for additional colors of clousers, and bucktail or “traditional” deceivers, glass minnows as your budget allows:
Thread: black, white
Bucktail: white and olive or light blue
Topping: a pack of strung Peacock Herl 3 bucks
Body: Pearlescent body braid 2-3 bucks
Optional: pack of white strung saddle hackle 3 bucks
Using these materials plus some additional hook sizes and inexpensive material and you can tie a whole host of stuff for your local waters to imitate everything from shrimp/crab flats stuff to big baitfish patterns for whatever you’re chasing, as you build up an inventory.
As far as SW tying DVDs, you might be better off searching for specific patterns you want to tie on Youtube and step by step tutorials on the web for free. But Scott Sanchez has a good intro book:
Amazon.com: Introduction to Salt Water Fly Tying: Scott Sanchez: Books
We can also point you to a bunch of SW tying sites if you have some specific patterns in mind, or want to let us know where you’ll be fishing and what you’ll be chasing, folks here could suggest some patterns to start with.