It would be hard to beat a Previa for someone minivan-shopping on a small budget. True, you could get a Ford or Chrysler used that was cheaper, but it won't last, and will likely have problems the whole time.
Keep in mind that the newest Previa is almost 10 years old now, so even as good as they are, you are still likely to have occasional problems especially buying a vehicle unknown to you.
The crash tests gideon mentioned are a bit misleading: When the government and insurance agencies switched their tests in the mid-1990s, the Previa, which had previously had good test marks, suddenly tested poorly. Reason? The new tests are called double-offset, which are supposedly more like real-world crashes. The old tests, under which the Previa originally was certified, was where the vehicle crashed full-on into a barrier. I still drive my van and don't worry about crashing. It's a point to consider when buying a car, but would never be the deciding factor for me. If your kids ride in the middle seats where they are supposed to, they will be as safe as can be expected in a crash.
The engine in the Previa is bulletproof; they can go over 300K without overhaul. People who lose their engine before that either do only stop-and-go driving or don't service their emissions system.
Beyond that, there is no particular year that is better for the Previa: They are all good years!!! What is important is choosing what features you want. The primary differences are: All-wheel-drive, supercharged engine (same engine, but with a bit more power), manual transmission (there were VERY few of these sold) and basic or luxury models. The Previa ranged in price from 22K to almost 40K by the time sales stopped over here because they are very well-designed and well-built vehicles. The loaded, leather-interior, AWD, supercharged ones still command a premium, and are worth the price IF they have been serviced properly.
My Previa (below) lists for about 3K, but is well below average miles and is in very good condition for its age, almost 16 years old. If you are looking for the best value in Previas, look for 1991-1993; they are the first generation, non-supercharged vans. You can get AWD with them but those might be a bit underpowered. My van has plenty of power for my uses (not hauling bricks & lead blocks; just people & gear) and I never have to slow down except on really steep hills where many other cars do as well.
If you want a little more zip, get a supercharged, RWD model. They put out more power than mine.
If you need an AWD model, make sure the owner always changed all four tires at the same time. Different-sized tires wears out the AWD mechanism prematurely, and it is expensive to replace.
Finally: Yes, the Previa is cool! I'm a single, no-kids guy who is probably the last person who would buy a minivan, but when I rode and drove around in it with its prior owner, a close family member, the van really grew on me. I get compliments all the time from people on it, and the styling still looks fresh and modern even though it was styled in the late 1980s. It does have some minor crankyness due to its age, but overall has far less gripes than even some new cars these days.
Good luck with your hunt. I suspect there are many Previas to choose from in the Puget Sound area, so be picky & let us know what you find!!!
C