We did string bags and I absolutely dislike them because I can't fit my warm ups, grips, water bottle, and shoes and other stuff like hair stuff in my bag during the competition! I say go for a duffle bag or a backpack type bag
They didn't have a jacket embroidered for DD this year because it's a small team and the booster club just forgot I guess. We bought a Champion jacket, and black capri leggings from Target and she looked fine. I know many disagree but I don't think clothes make the team. If they are matching and neatly groomed with maybe a homemade scrunchie and matching flip-flops also decorated at home in team colors, they look great.
I vote backpacks. They are hands-free, there are usually enough smaller pockets, and even the little, spindley-legged boys seem to carry twice their weight. I once found my child had been carting around the entire season's medals...everywhere.
Also, they can be hung over the backs of chairs for the great, passive-aggressive, chair-stealing event that precedes all lower level meets...