In order to choose the correct recessed lighting housing, you will need to know whether to use a remodel or new construction style housing. Although these terms seem straightforward, they are somewhat of a misnomer.
New Construction Housings are appropriate when you have accessible space around where the light is going to be placed. These are used when:
You are building in a new space where you have full access to the wall/ceiling/floor without sheetrock or plaster hindering your access to beams, etc. Or you have access to the space due to an overhead attic, a pop out ceiling panel, etc. The reason you need all this space is that new construction housings are bulkier and are installed in between joist beams or onto hanger bars from T-Bar or drop ceilings.
Remodel Housings are less bulky and appropriate when you have limited or no access to the space above the new fixture. This is common in apartments or homes without crawl spaces or attics. Remember, even though Remodel housings are less bulky, it does not mean that you won't have to remove sheetrock or make holes in your ceiling to accommodate your new lighting plan.