Ported boxes are the best compromise for sound quality and output efficiency. Sealed boxes usually have the best sound quality and frequency response, but also make the least efficient use of amp power. Ported boxes can sound almost as good, depending on box size and port tuning, and make pretty good use of amp power. They tend to be more narrow in frequency response because of the port tuning though. The type of port doesn't matter, slot ports don't sound different than anything else, but they're often convenient because they allow you to put a large or long port in a fairly compact space on/in the box.

Bandpass boxes have the most output for the amount of amp power, but also have the worst sound quality and the most narrow frequency response. They tend to be "one note wonders". I'd stay away from bandpass boxes unless you only listen to hip hop or something without much frequency range. "Bandpass" means they have one narrow frequency response range, and the response falls very sharply above and below that frequency range.