I don't really have a preferrence for types of latex and have used many types including Benjamin Moore, Glidden, Sherwin Williams, etc... When I paint those types of doors, I keep a rag and a bucket of water next to me. The reason is that the paint dries too quickly (like other's have said above), so I need to wipe the excess off as I go. Usually, I'll paint a square panel and then wipe the wet paint off the styles that separate the panels. I'll then repeat this procedure until all six panels are painted. From there, I'll paint the style separating the two top panels and the upper style as well, then wipe off the excess paint on the side styles and middle style between the two middle panels. I repeat this procedure on every style until the door is done. I don't know if it makes sense the way I'm describing it, but basically I paint each piece of the door separately and wipe the excess off the other panels. It's the only way that I can do it and have the paint lines going in the way that a wood door would have and not have thick, globby paint areas.
Spraying is the way to go if your looking for perfection but it's not always available or worth the aggrevation to rig up a sprayer for a couple of doors.