The function of a goalie neck protector or throat protector is no mystery; they are made to protect the neck and throat of the goaltender. "Danglers" and throat collars/bibs protect the same general area, but they are easily distinguishable by design and they protect the neck/throat of the goaltender in different ways.
These types of neck/throat protectors are called danglers because of the way that they dangle from the bottom of a goalie mask. Danglers are constructed with highly durable plastic (Lexan) that is strong enough to withstand direct puck impacts, but the design is, of course, most effective when the puck is deflected away from the goaltender upon impact, rather than absorbing the full impact of a direct hit. This is accomplished by leaving just a little bit of slack on the strings attaching the dangler to the mask. If the strings are pulled too tight and the dangler isn't actually dangling, and is instead just tightly bound to the edges of the mask, it will absorb a greater amount of the shock than it ought to.
Danglers are offered in different styles or "cuts", like the half shield visors worn by players. The most important thing to remember is that you're trying to protect yourself as well as possible, which means that you ought to try to find a dangler that leaves the smallest amount of your neck exposed as possible. Because of the simple design of a dangling throat protector, there isn't much to worry about in terms of mask/dangler compatibility, although, you may find that certain types work better for you than others, offering a more desirable blend of protection and mobility.
Bibs & Collars
Bibs and collars are constructed with nylon containing foam padding and, often, plastic or Kevlar inserts. Kevlar is also sometimes used in the outer lining of the collar to protect the goalie from being cut by skates and sticks. Protection from cuts is the sole purpose of the throat collar or bib. Bibs and collars will deaden the blow of a shot to the neck or collarbone, but they shouldn't be relied upon for this type of protection because a significant amount of shock is likely to make it through the protective layer.
Goalie throat collars and bibs vary from model to model in the amount of protective coverage that they offer. Some throat collars are just slightly more protective than players' neck guards, with minimal collar bone and upper chest protection. Other throat collars and bibs are more heavily padded and offer greater overall coverage to the collarbone area and upper chest. Finding the bib or collar that works best for you will depend upon the amount of protection offered by your C&A protector, as well as the amount of mobility/breathability that you desire. That being said, you should always choose the throat collar that is best-suited for the level of competition at which you're playing.
Protect Your Neck
As a goaltender, your neck is one of the most vulnerable parts of your body. Even with proper protection, in relation to the protective coverage on the rest of your body the neck/throat is likely to be the most exposed body part. Neck protection has come a long way in recent years, especially with the implementation of high quality, cut-resistant materials like Kevlar. You can never be too careful; if you witnessed the life-threatening injuries sustained by NHL forward Richard Zednik and former NHL goaltender Clint Malarchuk, you know just how quickly a seemingly harmless game can turn into a race to save someone's life. On separate occasions, both Malarchuk and Zednik had their throats cut by another player's skate and lost a substantial amount of blood on the ice before being rushed to the hospital for emergency surgery.
It's very important to understand that in order to properly protect your neck, you ought to wear a throat collar/bib and a dangler. We've gone over the different types of protection offered by each, making it very clear that when either one is worn without the other you are putting yourself in danger. Pucks, sticks and skates are equally capable of causing serious injury to your neck and throat, so make sure to wear equipment that will properly protect you from the various dangers posed by each. The threat of serious injury can't be completely eliminated, but it can be substantially diminished.
It's hard to go wrong with neck protection, but I suppose it's possible. The key is to make sure your neck, throat and collarbones are well protected without being constricted or restricted from moving comfortably and freely. Throat collars and bibs typically come in Junior (13 & under) and Senior sizes (14 & up) and can be adjusted easily with the loosening and tightening of a Velcro strap.
Danglers aren't really sold in "sizes", but rather they are offered in different shapes/styles/cuts, as noted above. Affixing a dangler to your goalie mask can be done a few different ways. You can use the ear holes on the sides or the bottom bars of the cage to tie on the strings. Some people believe it's best to let it hang loosely on all sides so that it doesn't limit your head/neck movement. Others prefer to pull the strings tighter and keep the dangler close to the bottom edges of the mask, which prevents it from clanging around and holds it closer to the goalie's chest when he's looking down at his feet trying to find a loose puck. Either way you go, it's a matter of personal preference. All things considered, protection should be your primary concern.