"Middle class," by any reasonable definition, is a wholly anachronistic concept when speaking of the Roman world, and really doesn't get us much of anywhere. More useful, in a thoroughly agrarian society like that of the Roman Mediterranean, is the distinction between landed and unlanded individuals. Now, it's true, a large portion of the Roman population held their own little plots of a jugerum or two throughout Italy. These small-time farmers held just enough property to be largely self-sufficient (barring a bad harvest, always a constant threat in a pre-Green Revolution society) but not enough to be considered wealthy by any margin. "Middle class" would be an improper label for them, however, in that they were a localized farming class with few similarities to the modern "middle class" except in that they were more or less economically self-sufficient. Moreover, a scenario in which such a small-time farmer would find "nothing to eat in the house" is rather unreasonable--such a situation would likely only occur during a bad harvest or other circumstances of extreme economic duress.

What we really want to look at, then, is the city, for all kinds of reasons. But within the city the economic disparity between the landed and unlanded becomes so stark as to leave little room for anything resembling a "middle class." The vast majority of urban dwellers were semi-itinerant day-laborers, seeking work at the monumental building projects, the Tiber dockyards, suburban fields, etc. on a daily basis. There was never anything resembling a fixed wage at Rome, but we can extract from our evidence rather good reasons to suppose that for the "average" worker in the city it was only barely possible to provide the money to feed one's family, after the high cost of rent in the city. So as not to reinvent the wheel, I encourage you to read through this thread, which should give you an idea as to the realities of living in the city for the vast majority of the urban population. A relative few, the so-called plebs media, owned their own shops or workshops, and could rely on a steady source of income, however slight. These individuals were also generally not landholders (though sometimes landholders, especially senators who legally could only own businesses by proxy, set their own slaves or freedmen up in such trades and took a cut of the profits) but could pay their rents steadily and could afford permanent lodgings, unlike most day-workers, who were probably forced to change tenements rather regularly, either from an inability to pay rent or to chase work in another part of the city. To speak of such individuals as being a "middle class" misrepresents their place in society, however. They were above the mercenarii that made up most of the city's population, but only barely, and though they could close down their shops (or leave them to their workers and slaves) for a day or two to participate in political activity or festivals and maintain some degree of economic security, they still generally had dangerously little in the way of savings, and had nowhere near the economic power of the modern middle class. In any case, most urban dwellers, day-laborers and shopkeepers alike, did not live in circumstances in which one could realistically find "nothing to eat in the house." The urban population lived in cramped insulae, which were extremely dangerous and in which the urban plebs were packed family-by-family into tiny, cell-like compartments. Insulae had no hearths, and thus tenants could not cook inside them even if they wanted to--an insula was a place to sleep, and little more. The urban plebs, therefore, lived generally outside their tenements, and survived on food cooked outside. At communal ovens and by paying for the services of bakers the urban plebs could turn the wheat they bought or were distributed into bread, although Purcell has shown that most urban dwellers survived mainly on a sort of porridge rather than bread, which was too expensive for most of the population to make. The "average" urban dweller, living in a tiny insula without any landholdings of his own and likely with no steady income, would not have been able to conceive of a situation, save owning his own domus, in which he might be able to cook his own food.

On the other side, those who owned their own property were, in the city at least, almost invariably fabulously wealthy. Property was at a premium in the city, and urban domus were exclusively the possessions of the equites (really just wealthy plebeians, although under the Principate they became a distinct ordo) and the senatorial class. While we hear of people like Caesar and Sulla, who began their lives relatively impoverished, these individuals were aristocrats with hundreds, if not thousands, of clients and dependents, and estates throughout Italy. They may have had a lack of ready cash (land is not so easy to liquidize) but the sum of their assets would have dwarfed the means of the urban plebs. For people who could own property in the city, invariably their own domus, often quite extravagant, there was always food available inside. These wealthy individuals had, at the very least, a few slaves and hired workers to run the house, and in particular the kitchens--the equites and senatorial class did not cook their own food, and they did not worry much about their own provisions, leaving it to someone else. Owning property in the city was a considerable investment, one that continued to eat up money in the form of maintenance, provisions, and wages for workers, and it's unrealistic to imagine anyone but the very wealthy owning their own urban homes.

All this aside, what options did exist for "street food," so to speak, in the city? For the urban plebs really everything was street food, in that all of their meals were prepared out-of-doors, often by someone else. For somewhat better meals than a bowl of emmer puls (basically warm mush) or bread there were thermopolia and popinae available. The former are basically sit-down establishments with a decent amount of room and, usually, long bars on which were placed cauldrons filled with whatever the owner felt like filling them with. They're all over Pompeii, a quick google search should give lots of examples of really rather nice ones, with stucco'd countertops and even frescoes. The latter were sort of little food stands, usually permanent rather than something like food carts, that sold pastries and other items that could be eaten on the go. Both are rather well-attested in literature as being places that educated people like Juvenal and Martial might go, and from what little evidence we have it doesn't seem likely that the urban plebs spent a lot of time in such places, whose prices were probably unreasonable for most day-workers, whose lives were more or less hand-to-mouth. As Purcell notes, for most of the urban population the supplements to their diet of wheat, either as puls or bread, were mainly nuts, chickpeas, and fruit (dried or fresh), which could be picked up relatively easily at markets while passing through on the search for work whenever laborers had a little extra money left over.

By middle class, what do you mean?