Pay no more the 5k, start at $4500
The oil burning was with the 2.4 engine not the Sienna. Now, you would want a mechanic to check it out BEFORE purchase. If they don't let you, walk away. If you are in California or someplace where cars are expensive, don't pay more than 5500 or so. If you are somewhere else liek Texas etc. I would shoot for below $4500 and start at 4000.
No, the Sienna doesn't have the oil burning or fuel pump issues. Infact, Scotty has repeatedly said that the Sienna is the best minivan on the market. I would jump on that van if I were you. The Sienna and the Quest are like night and day.
A 2006 Sienna is an excellent choice for a minivan. I have a 2006 Sienna LE with 115K miles and it's been great - I just finished a 2300 mile roadtrip with it and it was perfect. The 2006 Siennas with the 3.3L engine do use a timing belt that needs to be changed every 90K miles, so check to see if that's been done. $6K is a reasonable price for the van if it's in good condition - the Siennas always go for more money than other minivans. If it checks out mechanically, I would certainly go ahead and make an offer.