I like to wear the briefest that I can buy locally. Many years ago I could get briefs that were like two small triangles of thin material that met at the side. I liked them because they were comfortable and left my legs free to move. Unfortunately they went off the market and I had to switch to more bikini style but I always look for the briefest. They aren't always available so I buy a bunch when I find them.
Generally I wear next or OddBalls briefs (I love the bright colours and crazy designs of the OddBalls). Occasionally wear trad style baggy cotton boxers - so loose that it feels like freeballing and at other times I freeball.
I tend to go through phases when I'll wear briefs for a few months, then boxers for a few weeks, briefs for months, freeball for a few weeks - you get the idea. Currently I'm in freeballing mode but that'll change before too long
I like the idea of wearing a jockstrap, but the reality is that it's clothing and I don't like it.
I don't even own any underwear -- thus, I don't wear any.
I do own a jockstrap, but it's more of a novelty item than a piece of clothing -- and I essentially never wear it.