We did this on our last cruise, and it took about 10 minutes. They verified the download before handing us the disk. The one caution I can give is that it downloads still files only. We lost our digital video because I didn't realize that they hadn't copied over. It is possible that they could have transferred the video, but I didn't think to specifically mention the video, so they didn't know there were video files on the card.
As far as the type of memory, we had the sD card, but I think they can handle any normal type of media. And since most CDs hold well more than any card I can think of, I can't imagine that your card size will be a limiting factor. If you're still concerned, stop by Shutters during the first day, and they'll be happy to go over what they can do. That way, you'll know if you have to stop at 500 pictures if that's a limiting factor.