I have heard good things about the Graco double strollers. I have no personal experience with them though. As far as diaper bags, we used a regular backpack with 2 outside pockets and a suede bottom for our last trip. If you really want to go with an actual diaper bag vs a backpack, I recommend you get one that is the canvas type material, not the plastic sort of material or liners most commonly seen. The plastic tends to rip or break up over time. We currently use an Eddie Bauer diaper bag, I think I got it at Walmart, and have also seen them at Target. I forget how much it cost, but I have had mine for a couple years now and it has held up well. They also come in 2 different sizes, we have the small size one, as it works well for us and I hate hauling around one of those huge bags. Although the huge size is available and I have seen lots of people carrying the huge bags around, just not my style. If you really don't want to carry a huge bag, put the diapers in a plastic bag and just leave it in the bottom of the stoller, any other essentials, like bottles, change clothes, etc you can put in the diaperbag. My thought was if someone was so hard up for a few diapers they were welcome to them, I did carry a few in the diaper bag though, just incase the others disappeared, but they never did.
Oh, our small diaper bag has 2 smaller zip up compartments, one on either end, mesh areas on both ends and the front (don't hold much if the bag itself is full though) and then one middle compartment with elastic bands in it to hold bottles, or what not. don't recall how the larger bag is set up though. Our bag is navy blue, and I have also seem them in hunter green.