I'm convinced there's not a "good" minivan on the market, they all have problems, rather it's transmission problems, poor MPG, uncomfortable seats, or squeaks and rattles. Every van out there is a compromise in some way, Honda and Toyota have fewer problems, but they're still not as reliable as any compact sedan on the market. Roll the dice and hope you're one of those guys who never changes the oil and never has a problem, I know I'm not that guy. When I bought a '01 Sienna with just shy of 100k miles, I expected it to be as reliable as a Camry or Corolla, I had it in the shop within a week of buying it and it continued to have problems as long as I owned it, in hindsight I should have taken it back to the dealer when the first problem came up and bought something else.
We ended up selling our Sienna and bought a Chevy Astro that is a couple years older but has lower miles. It's a compromise as well, it's got MPG to rival the Hyundai, it handles like a truck, and it looks like a brick, but we like the extra space, my wife likes sitting up higher because she can see the road better and I like that I can tow a utility trailer and not look like a complete tool. I do expect it to need ball joints, tie rods and an idler arm in the next year or two, but every astro van needs these items replaced so parts are pretty cheap and it's something most shops will know how to do, or should I choose to do the repairs myself there are good instructions on line.