Large Copper Ancients

Nice big beautiful sestertii of Rome can be had for under $100 (30-35mm) Nice guys cost less. Big Big Ptolemaic bronzes in the 40-45mm range can get expensive. Several hundred at least for a nice one. Smaller 30mm would be 'proportionally' less. A nice silver dollar sized Ptolemy might be had for around $100.

As with any other type of coin condition is going to determine what you will pay for the coin. You can find some fairly nice sestertius for under $100.

Other than two classes of bronze coin mentioned, the only other classes of large bronze coins that readily come to mind are magnificent Russian 5 kopec pieces and the pure copper British 'cartwheel' twopences.
These are not ancient, but sit nicely in a collection of older large OFEC bronze coins.

There are quite a few large bronze pieces of the 19th century. Turkey issued some, up to 40mm diameter, the Vatican issued some remarkable 5 baiocchi and 4 soldi pieces, Ceylon issued a nice 5 cent bronze piece in 1870, Portugal issued large 20 reis coins for themselves and for thae Azores and a 40 reis piece, that must weigh nearly two ounces, and the Chinese issued some scarce 5 and 10 cast cash coins with a square hole, which were over 30 mm in diameter.

These sorts of coins make the subject of World numismatics quite interesting.

As an oddball, I have seen a Burmese bronze tamlung, of 4 bahts weight of the 17th century, of the
Eastern Toks of Nan, in an auction catalogue. It had an estimate of $30. This piece is anepigraphic, with a small blob of silver melted into it, which gives it it's circulating value. If you can find one of those, best of luck!

All of the coins I have mentioned would cost $50 or less in VF condition.

If you go with 'nice guys' (Antoninus Pius or Marcus Aurelius) a fairly decent 32mm Sestertius can sometimes be found for $30 but you will need to follow ebay listings and make an effort to sniff out 'bargains'.