The bags at Promotional tote bags custom sizes and styles from cheap totes are good. The thing is, how much stuff do you want to lug down with you?
The boxes are okay, but people will throw them out. If you want something they can use again, go with cheaptotes. Their bags are around 99 cents each and don't smell.
I would say just order them from cheaptotes if it is something you want to just get crossed off your list. The prices don't go down past 99cents. The woven bag from target is cute, but if you are making 20 bags, that is A LOT of bulk. You have a baby (that I assume you are taking with) babies have enough to take. Why stress yourself out with OOT bag stuff?
You can make a transfer onto iron on paper and iron them on the bags, or get pre-made iron ons and use those if you want to jazz up the plain bags. People will use the bags versus the boxes. We always saw our guests with our bags, carrying around their miscellany stuff.