The basic options for braces are metal (stainless steel) or clear. Metal braces are the most common. They come in a myriad of shapes, sizes, and features. Every orthodontist uses a system that they feel comfortable with. Some offices try to save money by recycling metal braces. I don't do this.
Clear braces can be made out of plastic, composite, or porcelain (ceramic). I don't use the plastic ones. They are cheap, but they stain, wear out, and become useless. Composite is more durable than plastic, but they also wear out over time and become useless. I use ceramic clear braces. These also come in many shapes, sizes and have different features.
There are two basic types of ceramic braces (brackets): monocrystalline, and polycrystalline. Monocrystalline brackets are clear like glass, but they are prone to fracture. Polycrystalline are tooth colored or white, and are much more durable. I use polycrystalline ceramic brackets.
There are also "Lingual" braces, which go on the insides of the teeth. I don't do these. It is a much more time consuming, costly, uncomfortable technique that I have no use for (I only did one case, and it was not pleasant for either me or the patient).