Hmmm....that's a good question. The first thing my mind goes to is a sestertius, which would be 32-34mm in diameter. That said though....I don't know what your price range on this project is and sestertii can be a little expensive. Asses and dupondii are also good sized copper coins. They range from 27mm to 29mm and often cost less than a sestertius. Another option would Constantinian bronzes. They can often be purchased fairly inexpensively and the AE1's are over 25mm and the AE2's range from 21-25 mm. You said something large enough to see, so my favorite, the denarius, is likely out of the running. They're about the size of a cent or a dime, but they are silver, quite affordable and often extremely beautiful. As for myself, I'm not a fan of the Constantinian bronzes as I like the more classical era of Roman history. Another thing you have to consider is the ruler on the coin...that can make a huge difference in price. I know that this is Wikipedia, but there's a good picture on the page that shows examples of the different denominations you will run across:
https://en.wikipedia.org/wiki/Roman_currency