I use a hard shell, rolling carry-on.
Going to the game, my uniform is folded. All of my flags, bags, whistles, etc. are in plastic bags. My shoes are in a shoe bag. Everything fits in the hard shell carry-on, along with my hat in a cap-caddy.
Going home is about the same, but my uniform is now in a dirty garment bag.
I carry a separate bag (historically a messenger-style bag, but this year I'm switching to a small backpack) that has foul reports, game cards, rules/mechanics books, quizzes, notes, etc.