I haven't noticed any major difference between brands. As for size, I use whatever size seems the most reasonable for the job at hand (limited to what I also happen to have available at hand). Since I tend to do some pretty fine-pitched stuff, I generally prefer the smaller sizes, usually just about the width of the iron tip, give or take. It's not very critical.
Hi,
I use the same method as SamR.
It also helps if you use a safe liquid flux to partially flood the wick strands just before desoldering the component.