Fuel-efficient with lots of storage

If you're set on a minivan, the data on this site would support getting a Toyota Sienna. The Odyssey seems to be almost as good with the Sedona trailing a little behind that in terms of reliability; although certainly the Sedona will drop value faster, so maybe a '12 Sedona with less miles would be comparable to an 09 Sienna that costs the same? I would stay away from the Chrysler products - their data on this site isn't as reliable and anecdotally, I've known folks who've driven them, and even during the lease period, little bits and pieces seem to fall apart.

I don't know the exact volume of your stuff, but if it would all fit in a smaller vehicle, you would save a lot of money over the cost of ownership of a minivan. The likely smaller candidates would be a Honda Fit or a Mazda5. The Fit has about 2/3 the volume of a minivan behind the front two seats, but the passengers seat can also fold flat. Very easy to reconfigure; cheap to maintain; 35+mpg. The Mazda 5 is a little bigger and has 3 rows of 2 seats but is more streamlined and cheaper than most minivans; 25mpg. Your budget would get you a brand new Fit (with a couple thousand to spare) or maybe a year or two old Mazda5.

Another larger option might be the Ford Transit Connect. It's a van-type vehicle on a Ford Focus platform. I hear the seats are kind of a bear to wrangle, but they're cheap, voluminous, and get OK milage. A new or year or two old model might be cost competitive with a 5 year old Sienna/Odyssey.

Whenever people say they want a vehicle that will be reliable for ten years, I'm inclined to recommend either a Honda or a Toyota. The choice between the Odyssey and Sedona comes down to personal tastes and priorities.

The Chryslers and the Sedona are iffy for this long a time period.

The Ford Transit Connect is definitely worth a look. It's too early to know how reliable they'll be, but they are engineered with commercial use in mind. The seats are finnicky, but it sounds like you'll just leave them folded most of the time anyway. The long version can haul a lot of cargo. Handling is considerably more nimble than a regular minivan. Fuel economy should be a little better than a regular minivan. I'll have more details after I test one for a week in late March.

There's much less cargo space in the Mazda5 also suggested above, so that one will depend on how much space you need. Same for the Honda Fit, which has even less cargo capacity.

First step is to figure out how much cargo volume you need.