Come on over to the anime thread--I think people will be more than happy to discuss this with you there =)
That said, Dragonball Z's character arcs don't even make sense without Dragonball to create the grounding for them. I say this, of course, as someone who has only read the manga, so I'm most used to seeing things that way. To me, the plot line has never been about the external enemies (often soon to become friends!), but about the internal battles, and why and how they are waged. Without starting where everything started, it's hard to see how it all fits together.
But sure, I'll bite.
My favorite character... in light of all that, I don't have a favorite character. I used to identify heavily with Vegeta. It isn't just that his entire identity is trapped in one thing, or that he constantly loses, but that he can't see his friends treating him well. He gets angry and thinks they're blowing him off. He sees other people's love for him and can't deal with it, because the way he sees things doesn't admit it as worthy or important. And finally, at the end of everything, in order to become whole he doesn't just have to accept his position of constant corporeal self-sacrifice, but also has to toss away everything he once understood. The Saiyans don't die when he does, or when the planet explodes; it's an end of their ideals that has to occur for their last surviving prince to live well. In some ways, the story is a classic tragedy, with the hamartia here being pride. Luckily he got a chance to become something else, but all the same I've always been touched by it--particularly the part at the end when he unexpectedly receives heavenly grace, having abandoned absolutely everything but the unselfish wishes in his heart for the good of all beings.
Secretly, I root for Gohan and Kuririn to be happy in life. They don't get much in the way of breaks.
Favorite fight is definitely the one with the Potara earrings. You know what I'm talking about. That was hilarious. For the actual fight itself, though, I tend to like all of them pretty well. I don't have a favorite part for humor, though... I've always thought the entire thing was written in a very tongue in cheek way, so some days the entire thing will seem absolutely hilarious and absurd, and at other times I'll be really saddened by it.
... Battle outfit... ? I always liked the Kaioshin coat.
The best mode of transportation is definitely Kinto-un, hands down, though Buruma's spaceships are pretty cool, too.