As an avowed NON-minivan owner you'd think I have no business on this thread. But I AM an auto enthusiast and keep up with that world, and have several friends who own minivans.
From what I hear:
Honda Odyssey usually wins in an all-around contest. Resale is almost certainly the best, as is reliability (par with Toyota?) and the current model is said to 'drive like a car'. As you must know, that's a good thing, particularly when it comes to safety.
Sorry to dis the Chrysler/Dodge owners here, but that is the last minivan (or any car) I would choose. They have always had problems and if my experience with a few rental cars, including an older van are any indicator, they are pretty lousy at the driving experience too.
Also noted that someone mentioned VW. Nice looking BUT be aware it is a Chrysler in disguise! C makes them for VW. A friend recently rented one and he was VERY disappointed in the driving experience.
I'd say the best thing for you to do is gather info (eg from Consumer Reports and such) about reliability, pick the top 3 of those that fit your budget, and drive them to see which suits your style. Because it can be argued that minivan reliability is a bit more important than for other cars as they often contain kids, and are often driven by women, and women USUALLY know less than men about repairing autos. This is NOT a dis to women, it is simply a widely-observed and generally agreed upon phenomenon. I could write a book about ways women are superior to men too.