Looking at flotation devices (life jackets) they are rated Type I, Type II, etc. What do these rankings mean and what type should I by?
The system of ratings for Personal Flotation Devices (PFDs) was developed jointly by the United States Coast Guard (USCG) and Underwriters Laboratory (UL) and has been in use for many decades. USCG had announced they were going to revise this system a couple years ago based on feedback from the public that they found the old system not understandable or useful. There has been no update about when a new system will be released.
A Type I PFD is also called an off-shore life jacket. It must provide at least 22 pounds (~100N) of buoyancy, must be able to keep an unconscious wearer face-up while in the water, must be reversible, and must be International Orange in color. They are intended for use where rescue is likely to be delayed. You will generally find them only on Naval and cruise ships, and are difficult to find in recreational boating stores. When you do find them, they are a bit more expensive.
A Type II PFD is also call a near-shore buoyant vest. It must provide at least 15.5 pounds (~70N) of buoyancy, and must be able to keep a conscious wearer in a vertical or face-up position in the water. These are intended when rescue is likely to be quick. They typically have a "horse collar" like appearance. They may be any color but are most often made in orange. These are very common and inexpensive, however most wearers find them uncomfortable for long-term use.
A Type III PFD is called a flotation aid. Like a Type II, it must also provide 15.5 pounds (~70N) of buoyancy; however, there is no restriction on how this must be positioned (in other words, it might not help the wearer remain face-up.) It is intended for use when rescue is likely to be almost immediate. These come in many designs and colors- often specially made for the activity such as paddling, fishing, water skiing, etc. They are the most comfortable to wear.
A Type IV PFD is a throwable device. Ring buoys, seat cushions, and the collar buoys usually carried by sailboats are all Type IV.
A Type V PFD is a special-use device. Typically, a Type V qualifies that same as one of the other wearable types but only when worn. The full-body suits worn by the crews of fishing vessels are a good example.
Note that the buoyancy and turning requirements for inflatable types are more strict than for traditional (kapok or foam) types.
In the US, your vessel must carry one wearable (Type I, II, III, or V) for each person on board, that is properly fitted for that person. You must also carry one Type IV for the entire vessel. Each item must be in good condition and "readily accessible" (meaning not in a locker/ bag).
Given you mention "type x" I guess you are referring yourself to the US classification. In other countries (like Canada or Europe) classification, requirement and approval is different.
So, for The USA, they vary in terms of application and buoyancy.
Type 1 has about 22lbs (~100N) of buoyancy and it should right you face up. Rescue wont be immediate and its effective in rough water (so if you know that you usually are in remote or rough areas you would get these rather than a type 2). Consider it offshore and its a lifejacket.
Type 2 would be about 15 and half lbs (~70N) of buoyancy, can turn you face up and think more about the short time rescue of inland water as its less buoyant than type 1. Its still a lifejacket.
Type 3 wont turn you face up in most cases, buoyancy is as the type 2 but they are more of a flotation aid than a lifejacket. Think whats used on kayaks and canoes: simple vest, no collar kind of PFD (In Canada they make a difference between a lifejacket and a PFD, as per buoyancy and turning ability differences. AFAIK the USA distinguish too in between a lifejacket proper and a flotation aid kind of vest).
Type 4 is for the throwable devices, Buoyancy here varies with the kind of device.
Type 5 is for the devices that have special uses, like for example collars, or suits with flotation. Buoyancy varies.
So when buying depends on your activity and the regulations (and these are a PITA when you got a boat from the US to stay north of the border and you have to buy all new lifejackets of the same model and brand just because they need the approval label for the specific country stamped inside).