Hi Manny,
Let's see if we can give a decent overview here, shall we? By the way, most of this info is in the stickies on this section, but we'll go through it here anyway.
Essentially, if we are talking Japanese Sword Arts, there's a few basic categories: Kendo, Kenjutsu, Iaido, and what I'm going to call Integrated Systems (systems that teach sword within their curriculum, although not as a focus). Let's start.
Kendo is a relatively modern sporting approach to Japanese Swordsmanship. It involves a split bamboo sword (called a shinai), and primarily consists of competitive training in which you learn the strikes that score points in matches, which are conducted with both combatants wearing a form of armour, known as bogu.
There are 8 legal strikes, to the left and right side of the body (do), to the left and right sides of the head (men, or yoko men), to the tops of the left and right wrists (kote), to the top of the head (men, or shomen), and a thrust to the throat (tsuki), all areas that are protected by the bogu. Besides the sporting side of things, you are also taught a series of kata, typically performed with bokken, although you may later use a metal sword, mainly for demonstrations that I have seen. This includes both long and short sword kata. Some schools may allow the use of two shinai in competition (known as Nito No Kendo, sometimes erroneously refered to as Nito Ryu and spoken of as Musashi's approach. It's not), although that is personal, and depends on the student as well as the school in question.
For this system you will need: Keikogi (uwagi, a training jacket), Hakama (wide-legged trousers), a Shinai (bamboo sword), Bogu (armour -that's where it gets expensive), and down the track a Bokken (long wooden sword) and a Kodachi Bokken (short wooden sword). Later you may want an Iaito or Shinken (we'll cover them in a moment).
Kenjutsu typically means a non-sporting approach. Believe it or not, there are modern forms of this as well, the most well known being Toshishiro Obata's Shinkendo system, and the Toyama Ryu (which Shinkendo is primarily based on), although the most common are the old arts (koryu). These range over a great list, including systems such as Hyoho Niten Ichi Ryu (Musashi's systems), Yagyu Shinkage Ryu (the school of the Tokugawa Shogun's teachers), Itto Ryu (the technical base for Kendo), and many many more. They range in approach greatly, having very large syllabus' or very small ones, depending on the system, and each getting across their own methods in their own unique way. These are not ewasy to describe, particularly if you have limited to no experience, the best is to visit any schools that may be around your area (if you are lucky enough to have a kenjutsu dojo near enough, that is...), and see for yourself. As Ken Morgan said here recently, many people are attracted to the sword arts because of their percieved "cool" factor, but few realise what is actually involved in getting any skill with them (thousands of repetitions of the same cuts and kata, over and over again, and so on).
For these systems, it will depend on the exact school you attend, but most will require you to get a Keikogi, Hakama, and Bokken. Some will also require a Kodachi Bokken, others will use a Fukuro Shinai (a bamboo sword cased in leather), and others will require an Iaito, Mogito, or Shinken. Still more may have specialist protective equipment, such as oversized gauntlets. A few may even request that you get a suit of Yoroi (traditional armour), but that is rare.
Iaido is a relatively modern solo sword art, focused around the drawing and resheathing of a sword. The "standard" version of Iaido is known as Seitei Iaido, which sometimes includes a further section known as Toho no Iai, a range of 5 Iai kata drawn from various koryu systems. Essentially, Iaido technique is broken down into 4 stages: Nukitsuke, Kiritsuke, Chiburi, Noto.
Nukitsuke is the action of drawing and cutting with the sword in one movement. This is followed by Kiritsuke, a follow-up cut/thrust/strike, or more. When the combat is finished, there is a symbolic/formal method of removing any blood or clinging particles from the blade, refered to as Chiburi (literally "blood shake"), which takes any of a number of forms depending on the techinque/system. Probably the best known (and what most think of when they think of Chiburi) is O Chiburi, a Big Chiburi, taken from the Omori Ryu. These kata are always performed solo.
Equipment for Iaido is Hakama, and a different form of Uwagi (jacket), although some schools may allow both uniforms to be worn. The expence here is the sword itself. You will often start with a bokken, however an Iaito will be needed (at least) pretty soon, and then probably a Shinken later on. The differences between an Iaito, Mogito, and Shinken is pretty simple. An Iaito is a metal bladed sword made from a zinc-aluminium alloy, which gives it a fairly close feel to a real sword, but it cannot take an edge, or stand up to contact. This makes it fairly safe for Iaido. A Mogito and a Shinken are steel swords, with the primary difference being that a Mogito is not sharpened (although you can sharpen it later on, as it will take an edge), and a Shinken (literally Real Sword) is sharp to the point of a razor, making it far more dangerous to use.
There are also a range of Iai systems which may use the term Iaido, Iaijutsu, Batto, Battojutsu, or just Iai, and may be more modern (such as Muso Shinden Ryu), or older (such as it's sister system of Muso Jikiden Eishin Ryu). These may be very similar to modern Iaido (as these two are), or rather different (such as Tatsumi Ryu Iai).
Integrated systems teach sword within their syllabus', although they may not necessarily focus on it as a primary weapon. Schools that teach a range of weapons and do focus on the sword tend to be koryu systems such as Tenshin Shoden Katori Shinto Ryu, Tatsumi Ryu, Kashima Shinryu, and many others. Systems that include sword in their syllabus but don't necessarily focus on it include Shinto Muso Ryu Jodo (which includes Kasumi Shinto Ryu Kenjutsu), Yoshin Ryu Naginatajutsu, Kiraku Ryu Jujutsu, Jikishinkage Ryu Naginatajutsu, Negishi Ryu Shurikenjutsu, and many more. There are also systems such as the various Ninjutsu-related organisations (Bujinkan, Genbukan, Jinenkan, and legit off-shoots), which include sword from the Kukishinden Ryu, Togakure Ryu, Koto Ryu, and others within their teachings. While the Genbukan and Jinenkan will be fairly uniform across all schools (the Jinenkan features the Jinen Ryu, founded by Manaka Unsui, and focused on Sword, Nito [two swords], and Jutte, while the Genbukan actually ranks seperately in Bikenjutsu), with the Bujinkan it is pretty much up to the instructor in question as to how much they integrate sword into their teachings. And none of these will be likely to just teach you sword by itself.
Another skill involved in the practice of swordsmanship, focused on greatly by some (Toyama Ryu, Shinkendo), and almost completely ignored by others (Niten Ichi Ryu, Katori Shinto Ryu) is Tameshigiri, or test cutting. This is cutting done to a prepared target, often a soaked tatami mat wrapped around bamboo, although substitutes are sometimes used as well.
But the bottom line here is one definate piece of information. If you want to learn any swordsmanship you will need an experienced teacher. There is no other way. So if you are interested in learning Japanese swordsmanship (or any kind, really), the first thing to do is find out what is nearby, and then visit as many as you can. Each individual school will often be able to help you out with whatever equipment they require you to get, listen to what they say in terms of the equipment. For example, if you end up with Niten Ichi Ryu, they use a highly specialised type of bokken, and regular ones simply aren't suited to it's practice, so if you were to go out and just get a regular one yourself, you may have just wasted your time and money. The most embarrassment I have heard of in these arts usually involves a student going out and buying a sword without consulting their instructor first, only to discover (usually when proudly showing it for the first time) that it was not necessarily an ideal purchase....
But an instructor should come before anything else here. Did that help?
EDIT: Hmm, a few got in while I was typing... er, what they said.
