Traditionally copper is used to forge habaki. Most of the time when you see habaki in gold, silver or any other material it is still just a copper habaki with a thin jacket of silver or other material over it. The style you pick is pretty much up to you. I like the yujo but i also like a lot of the niju style too.
I can't say much for the meanings of the different styles. As for material a lot of modern production swords have brass cast habaki.
I think the real issue you will have is the fit. Are you looking to purchase a habaki for a blade you currently own? Or are you looking to purchase a sword and looking for what fitting you should get? If you are looking to buy a sword it sounds like your looking at swordstore.com. They are the only dealers i can think of that offer habaki in silver or brass and shyonai or yujo. If you were buying from them, i wouldn't worry too much since you are getting quality regardless. It comes down to personal preference. Get what you like.
If you are looking for habaki for a blade you already own then you will need to send the blade to the maker in order to have the habaki made to fit the blade. The habaki is thought of as the heart of the sword and needs to fit the blade perfectly. Otherwise it can cause issues with the fit of the rest of the fittings causing defects in the sword. Habaki making is an art of its own.
Here are some nice yujo and niju habaki made in Japan. http://www007.upp.so-net.ne.jp/m-kenji/samples_of_habaki.htm