Get the motorcycle mount from island sanctuary.
Flat Cap hat is pretty good for giving the "delivery" vibe, if you don't wanna spend money. Red feather cap is also really good.
If you don't want to do motorcycle mount, there's a real nice chocobo delivery barding that you can put on your company chocobo, for riding around.
Far as pizza delivery goes, I'd opt for a casual look. Maybe go for a red and white dye setup, since pizza places tend to use those colors together. Back when I used to do an RP food delivery service, I'd opt for the casual jacket, any pair of pants, and a casual pair of shoes for extensive walking, along with the cap I mentioned earlier. Dye it until you look like your ideal. Ezpz.