wow triplets, you are in for it... we have twins and it's been no picnic the past 2 years... I can only dream of handling just 1 baby. You will have no free time whatsoever. We have a nanny in their grandma and even so, I barely have time to myself.
One thing to keep in mind with 3 seats across the 2nd row (since you can't use 3rd row at all)... they will be rear-facing for at least 1 year and you won't be able to tend to them so well. My wife sat in the middle with our twins so it worked out ok, but it will be tough for you guys - I'm guessing there will be those mirrors you tie to the headrests back there plus a few pull-overs on the side of the road and things like that.
I would go minivan without a doubt. The Odyssey's 3rd row is remarkably large. We would've pulled the trigger had it not been for a dealer unwilling to deal during cash-for-clunkers.
EDIT>> One other thing, sliding doors is a god-send on minivans... I can't tell you how many times I've had to back out of a spot to put these little buggers in their seats in the X. There's just not a lot of room for the door to swing open enough for you to stand there and do your thing with them. Now imagine others trying that next to your X... can you say door ding? Parking far away has been the only solution.