We've done it about every way possible. We fly and drive.
Driving: We buy the diapers by the box and would take one sleeve (any legneth of trip) of the 2 in the other 1/2 of the box pack all the baby food, dry snacks, etc since heh box has handles makes it tons easier to lug around. We'd pack whatever left over food and extras in the box for the drive home then recylce the box on garbage day.
Flying:
1. before they charged for every Kleenex you brought onboard I would use the extra car seat we had to check thru for the 'lap child' and strap in the pack of diapers and then bag the car seat in a car seat travel bag. I still do this but now pack running gear, or whatever into the car seat. There is no charge for the bag since it is technically a car seat as long as it's under the 50lb mark on any airline.
2. Ordered them thru wegoshop.com this has been fine as well
3. Picked them up at Publix using coupons I bring from home (least favorite but there have been times we had to buy more)
4.
Favorite-diapers.com we love that you can wait to order them until 3 days out track the shipment and there's tons of codes for $ off. You check in and they are waiting for you. I also order each child a Foogo for the parks and bring those home we can always use extras anyway, our kids are huge water drinkers. I order all our formlua thru them as well. You can get the 20% free cans from their site any extra formula I double bag up in ziploc gal bags and pour into the can when we get home.
For the flight I put them in nighttime diapers I have been stuck trying to fully do an outfit change on each child as a baby after leaking in our seats, good times

They drink more on the flight to keep ears clear and it has to go somewhere. I loathe changing in the glorified pot-o-let in flight. I've done it but there's something about your infant hovering over a blue liquid filled vaccuming hole that makes me gag. So I wait till we're minutes from boarding and do the last change then run for a change as soon as we deplane. Our flights typically run 2-2.5 hours max. I do take on extra clothes, just incase and travel with appox 10 diapers between carry-ons to make it thru travel and most of the 1st day in the off chance our diapers aren't wating for us tho that hasn't happened yet.