For the majority of my captures, I utilize Greatballs, for I happen to favor their look. For those more annoying to capture, I'd chuck Ultraballs at them, or stall for a while and use Timerballs. Luxaryball if I happen to like that particular Pokemon I'm capturing very much because I picture the insides of a Luxaryball to be luxurious and comfy. =)
Quickballs and Duskballs, although useful, were not the usual capturing devices I use.
Like some of the people here, I used to capture the signature Pokemon of the particular game I'm playing with Masterballs. Now I just keep them in my bag for my ball collection.
...No innuendo joke here. Really.