The easiest bag that I found on the internet: only two seams to sew to get a diaper bag that fits in your handbag. Nice to have, and nice as a small gift!
For the gray one I used a fabric with waterproof outside face so that I can use it as an underlay. I have used it a lot for short trips with the baby in the wrap or when visiting friends with babies. The red one with the umbrellas was a present to a good friend.
This is where the idea came from: youtube video.