Many different opinions here. I think most branded oils that are of the appropriate weight and meet Honda specified API standards are fine as long as you change your oil frequently (3500-5000 miles). I've used Castrol GTX in my 2002 with 170 k miles and oil changes every 5k and my last Blackstone oil report at 165 said the engine was running strong.
For the type of duty a minivan sees, I don't think synthetics offer a clear advantage over Dino oil to justify the cost difference.
With that mileage I would stick with normal dino oil. I did the switch to synthetic at 85,000 miles and all the seals started leaking. My mistake, I knew it would happen and just wasn't paying attention to which oil I used. That said, after replacing all the gaskets I've been using 0W-20 synthetic with great success and I don't have to remember to use different oils between by cars.