TLDR: Some plants have undergone extensive changes through selective breeding and no longer resemble their Ancient counterparts (wheat, and apples/carrots an extent, etc). Others simply didn't yet exist in the Roman diet (tomatoes, spinach, etc). But for the most part, you can plant just about anything you think would be found in a “Mediterranean” garden and be pretty safe.

Pliny the Younger talked about various agricultural villas, but only mentioned that one was "thickly planted with mulberry and fig.”

Cato the Elder, in his De Agri Cultura, said that “the best farm was a vineyard, followed by an irrigated garden, willow plantation, olive orchard, meadow, grain land, forest trees, vineyard trained on trees, and lastly acorn woodlands.”

The Lex Manciana, tax laws for the province in Northern Africa, talks about some staple foods: wheat, barley, wine, olive oil, beans, honey, figs. By that time, Africa was a major source of food supplies for Rome. The reason these foods were staples was in large part because they could be transported without spoiling. The delicate foods (grapes, olives, figs) were refined into something hardier (wine, olive oil, dried figs) before transport. This is typical for any farm outside of the general area of a city. At least early on in Rome, most farms were subsistence farms, owned by single families, and grew crops that could be both eaten now and stocked up for winter.

Only when you get closer to a city do you get more farmers growing luxury and perishable food (fruit, spices, etc). And these farms would be more likely to be owned by somebody else, and run by freedmen overseeing slaves/servants.

wikipedia has a list of possible crops:

artichoke, mustard, coriander, rocket, chives, leeks, celery, basil, parsnip, mint, rue, thyme 'from overseas', beets, poppy, dill, asparagus, radish, cucumber, gourd, fennel, capers, onions, saffron, parsley, marjoram, cabbage, lettuce, cumin, garlic, figs, grapes, 'Armenian' apricots, plums, mulberries, and peaches

Henderson, John (2004). Roman Book of Gardening. London: Routledge. pp. 40–65.

And there are many other lists of Ancient Roman cooking ingredients, like this: https://en.wikipedia.org/wiki/Ancient_Roman_cuisine

I'm casting my vote for a snail + oak grub farm. Don't disappoint me OP.

Fantastic idea, OP.

Jogged a follow-up question in my mind: would wealthy Romans have had decorative "exotic" gardens...perhaps plants from India, sub-Saharan Africa, or the Silk Road?

Note to OP: You haven't specified the climatic conditions where this garden will be located. This will affect the viability of specific plants.

The Getty Villa in near Malibu, CA has gardens that are intended to have plants that would have existed in Italy around the first century.

http://www.getty.edu/visit/villa/gardens.html

http://www.dailynews.com/lifestyle/20110618/gardens-of-the-getty-villa-in-pacific-palisades

I'm not a professional, but I may be able to contribute.

Apicius is a collection of Ancient Roman recipes.

While I'm not sure what a "typical" garden might contain, it seems reasonable that the ingredients used in the recipes would be found in at least some of them.

Book III focuses on vegetables. Some of them listed are:

• Asparagus
• Beets
• Brassica (various)
• Celery
• Leeks
• Turnips
• etc.

As others have mentioned, the cultivars in use today are almost certainly not identical to those in use 2000 years ago in Rome, but many may be functionally equivalent.

Well, if you want to add a bit of humor, you could grow cabbages and when people ask why you have them in there, you could say that one of the most significant emperors thought growing magnificent cabbages was a better way to spend your golden years than trying to hold together an empire that just didn't seem to want peace. It was Diocletian who said that, after retiring after 20 years of rule.

Edit:Diocletian, not Domitian. Domitian was never given the chance to retire

In 1982 the J. Paul Getty Museum published an excellent guide to the ancient Greek and Roman herbs now grown in their museum gardens (includes usages,) which include Basil, Bay, Borage, Chamomile, Coriander, Dill, Fennel, Garlic, Iris, Mint, Mustard, Myrtle, Onion, Oregano, Parsley, Rose, Rosemary, Rue, Saffron, Sage, and Thyme.

I'd recommend planting all but the Rue -- which is nasty invasive stuff that will try to take over your garden, and contains volatile oils that affect some much the same as poison oak. (Me, for example.)

ISBN number is 0-89236-035-6