If you haven't found a car yet, I would suggest a Sienna over an Odyssey for the added reliability and AWD availability. The Odyssey is also good and handles more like a big Accord instead of a boat like the Sienna. The Odyssey just isn't quite as reliable. I'd imagine the AWD option in the used Siennas are super expensive compared to the FWD, so make sure you're getting a good deal.
We've had a 2002 Odyssey since new and it has given itself a run for its money.
Yeah, the minivans are great because you can fit tall things comfortably and still have a lot of room leftover. The dogs could roam around in the trunk. If you don't ever have people in the back seat, you can take out the second row seats and expand the cargo area.
I'd avoid a used Chrysler/Dodge minivan because of reliability. The Sedona doesn't have as great of interior packaging and the old ones were pretty lackluster.