Welcome to the forums mikeps3.
What you are describing are the four major types of blu ray discs that are currently available (excluding the BDXL discs). BD-R discs can only be written to once, and come in two different capacities, 25gb single layer and 50gb double layer. And they have two different types of dye that can be used. The regular HTL discs use an inorganic dye. The LTH discs have an organic based dye similar to what was used in dvds.
The last type is the BD-RE, which uses inorganic phase change material, and it can be written to, then erased, then written again many times.
So, to break it down, most BD-R discs you find on the market will be 25gb, HTL discs using an inorganic recording layer. These are perfectly acceptable for most one time use, including the movies that you are asking about.
A BD-R LTH disc, using the organic style recording layer, is also 25gb (I haven't seen any 50gb ones, but they may exist somewhere). These are less compatible with older equipment, and there are some concerns regarding their longevity.
A BD-R DL disc is one that has two recording layers, and so it has twice the capacity, at 50gb. They are much more expensive, and you really need a compelling reason to use them. One such use is to get a complete blu ray movie backup without having to remove extras or compress the movie.
And I've already explained the BD-RE discs, which are re-recordable. They are not a good choice for long term storage, and they are slow to burn. BD-RE discs can be useful for testing purposes however.
The CAV, P-CAV and CLV notations you have there are referring to the methods used in burning discs at various speeds. I'm not the best to explain these, and if you want more information, you should inquire in the Lite-on forum or the Blank Media forum.
For best quality burns with BD-R media, you should probably pick something less than 8x speed. I burn blu ray at 4x usually, sometimes 6x with my newest burner.
The most important thing to consider with blu ray media is getting good quality blanks to begin with. I recommend the Smart Blu discs made by FTI Falcon as a relatively inexpensive choice, and Panasonic brand if you can afford them. Verbatim HTL discs have also proved to be good in my experience.