It depends on where you are in the Roman empire. Roman diet was necessarily reliant on local produce, but this would have been seen to a greater extent in the more humble diet of the commoner (general diets can usually be determined in dental remains, which again often confirm that people would have been eating what was readily available). This would include whatever fruits and vegetables were grown in the area, as well as what fish may have been available. Meats would have been more expensive, and as a result are more concentrated in high class diets.

The above only gives us a general sense of what was going on, though. First we have to bear in mind what resources were not available to the Romans! For instance, there were no tomatoes, potatoes, peppers, many berries and fruit, and of course corn (honestly the list is extensive, but I won't give them all here), as these are crops native to the Americas. It's also important to bear in mind that some ingredients, which were available to the Romans, were not typically eaten due to lack of interest (this is especially prevalent with Rice- with the first substantial use popping up around the sixth century CE, and widespread use following the Arabic conquests). Many spices only made their way into the Roman Empire in Late Antiquity, too, due to newly connected trade routes to South-East Asia. That said, many spices still would have been available to the Romans, but typically at a higher cost (Andrew Dalby has a few fantastic works which examine the spice trade in Antiquity, which can help to give a sense of the general accessibility to these spices).

Now if we are to approach the methods of food preparation, the Romans had a strong preference for boiling (be it stewing, simmering, braising, etc). This appears in their vocabulary in texts which mention food preparation (verbs like bullio, ferveo, elixo, decoquo, which all technically mean 'to boil', but all have various shades of meaning). This is also apparent in the cooking vessels which we have evidence of. In the late republic period, a vessel referred to as the olla (or sometimes aula) would have been fairly popular. It was effectively a big cauldron used for stewing, but could also be used for sauces. We also have mention of some other vessels coming into popularity around this period, like the caccabus (similar to the olla, but perhaps a bit smaller), and the patina (more of a sauce pan). A great examination of these vessels comes about in a PhD dissertation by Andrew Donnelly, although I'm not sure how open access that is (if you message me, I'm sure I could get it to you, as well as any other sources!).

Now I'm going to speculate a bit, and use a late antique recipe compilation (De Re Coquinaria, often attributed to Apicius, though I'm sure this is not the case) to look at Roman haute-cuisine. The recipes in here make use of various levels of preparation for single dishes, and as a result get a bit more complex of a result than a simple stew. For instance, the recipe for Vardanian Chicken (Apicius 6.8.11) has you poach chicken in a sauce, remove the chicken, and boil down the sauce. This results in what the recipe calls a 'white sauce', which it then instructs to serve on top of the chicken. Another chicken dish, Frontonian Chicken (Apicius 6.8.12), first has you sear the chicken, then boil it in a sort of broth. Once it's cooked, it tells you to remove it and serve with a seperate condiment (called defrutum). Those're just two examples of hundreds in this collection, but it is quite often to see a dish being served with a sauce. If my speculation is correct, then these recipes may stretch back a few centuries to the late republic. But otherwise we don't have a perfectly clear set of examples for high-class cooking.

So we get the sense that Roman cooking was separated by class, as you say. With the poorer individuals, I reckon stews and soups would have been more common, with simpler spices such as salt and black pepper, and perhaps some local herbs as well. They also would've typically featured resources locally acquirable, too (vegetables, fish, etc). There's also the issue of the urban poor, who would have been provided food via the grain dole in imperial Rome, as well as had access to 'street food' (at thermopolia- like the ancient Roman McDonalds, sorta). Higher class cuisine, however, would have made use of more complex dishes, often not being served in a broth as a soup or stew, but being plated with sauces and condiments.

I hope this helps explain it! If anything wasn't clear, or you have any questions on something I didn't touch upon (because this really is a huge subject), then please don't hesitate to ask! :)