2004 Sienna here - towing a 2100# VW Golf. 3500# tow capacity on the van. The U-Haul dollies weight around 700# IIRC. Tows fine at 65 mph with a tow dolly, just be sure and allow for looooonger stopping distances. If the dollies had the capacity for trailer brakes, I'd definitely go that route.
Class III hitch, purchased online from www.etrailer.com . Capacity and installation of all the Class IIIs they stocked was basically the same, I bought based on price (about $220, $270ish with the wiring kit). Also bought a set of air assist bags ($75 shipped) for the rear which helps to level and firm up the ride and gave a little more stability (there is some weight on the tongue, not much, but some) from Amazon ( http://www.amazon.com/LIFT-60732-1000-Air-Spring/dp/B000CFS028/ref=sr_1_1?ie=UTF8&... ) .
Installation of the hitch, wiring and airbags are within the reach of a basic home mechanic, the instructions were comprehensive.
The tow ball and the ball mount I purchased at the U-Haul place, since I wanted to get the length and ride height correct for the dolly. There are different ball sizes, so make sure you get the correct one.
Honestly, it tows better than I thought it would, gets 18mpg on the flats at 65mph (I keep it out of overdrive, not sure if that's necessary, but...). It also has the advantage of being able to fold forward / drop the rear seats into the floor to give a flat sleeping - I can camp comfortably at the track AND watch Cinderella on the DVD player!
I'd recommend frequent ATF changes, towing can get a transmission pretty hot. The Siennas of this era came standard with a "towing package" (larger trans cooler and fan) - if you don't have one, I'd recommend that also.
I do dream wistfully of something with a little more capacity, but at this stage it'll be a few years.