There were tons of different professions but the most common I imagine would be breadmakers. Most people in Rome lived in apartment buildings called insulae and would not have owned their own ovens. Therefore they had to buy bread (the main source of their calories) everyday from a baker. Many (perhaps most) Romans (people living in the city of Rome, not people throughout the empire) received vouchers for free bread from the government, it was that important.

So bakers, like modern bakers, did most of their work in the morning. First they needed to put charcoal in their ovens to make sure they are warm enough and prepare their dough. They presumably have someone to supply them with flour and another person with charcoal. They probably also needed an olive oil guy maybe a honey guy. I imagine they are using their own starter with wild yeast but maybe they get yeast somewhere too. So they would have connections with people all around Italy and maybe even the empire. Many of these bakers would be freedmen essentially renting their storefront from their former master and they may even get most of their supplies from their master's farms or his connections, kind of like a modern franchise restaurant.

So anyways, they get the bread in the oven and I actually imagine that their work would be done by the early afternoon (this again is just by comparison to more modern examples). Then they prepare the dough for the next day if it needs to rise that long.

Other overlooked professions: fullers (laundries) and tanners (make leather). I don't know too much about them (except that they both need a lot of urine) but hopefully someone can educate us on them too. Potters and blacksmiths would be common in other towns but in Rome most of their products were imported from other cities since the fire and smoke were noxious and dangerous and their products never perished.