Oh, boy. This is a complex, interesting, and somewhat controversial topic.
To begin with, we need to note that not all the sheathing metal applied to sailing ships' bottoms was in fact copper. Copper was the first metal that came into widespread use for that purpose. In the middle of the nineteenth century, though, copper ("red metal") started getting replaced by "yellow metal." This apparently took several forms, which probably varied a bit in color. "Muntz metal," introduced in 1830 (my source is George Campbell's excellent book, China Tea Clippers), was 50% copper, 50% zinc; in 1846 Muntz changed the formula to 60% copper, 40% zinc. Mr. Campbell says tin was somtimes added to the mix. Lloyd's Registers of the nineteenth century included notations on the sheathing of ships, and used abbreviations for "yellow metal," "copper," and "brass." (Brass, according to the dictionary I have in front of me, is typically 67% copper, 33% zinc.)
So what did it look like? Some modelers think - and they have some pretty impressive photographic evidence to back them up - that the manufacturing process introduced a considerable variation in color before the metal was put on the ship. In nineteenth-century photos of metal-sheathed ships on the launching ways, the individual plates do indeed look different - some much lighter than others. Some modelers replicate that effect by heating their copper sheets with a torch before cutting them into individual plates. I personally don't care for the result that technique produces; it makes the bottom of the ship look like a patchwork quilt. I also have a suspicion that lighting conditions had a lot to do with the color variations that show up in those old photos.
Anyway, when pure, bare, untreated copper is exposed to the atmosphere it starts to oxidize. Within a few months it acquires a fairly smooth, even patina that's a remarkably bright, medium green in color. (An historic house in the town where I live got a new, replacement copper roof about a year ago. It's already turned green.) Brass, when exposed to the atmosphere, turns black eventually, passing through various shades of greenish brown in the process. The proportion of the various elements in the metal affects the weathering process; so does any sort of surface treatment the metal received during the manufacturing process.
Michel's barrel is most interesting. I don't recall having seen a piece of copper that's weathered in precisely that way. I wonder if it went through some sort of chemical treatment at the factory, or if perhaps there's some additional element besides copper in it.
What did the bottom of a copper- (or yellow-metal-, or brass-) sheathed ship look like after it had spent some time in salt water? I honestly don't know - and I'm not convinced anybody else does. Part of the theory of metal sheathing was that the ship's movement through the water would constantly erode the surface of the metal, so fresh metal would be exposed to the water all the time. I don't swallow that entirely. We know that various forms of marine growth managed to hang onto the surface of the metal. (There are some well-known stories about warships being handicapped in sea fights because their copper was "foul.") I can recall seeing only one ship with a genuine metal-sheathed bottom that had been sitting in salt water for a prolonged period: the Charles W. Morgan. I'm not sure what kind of metal is on her bottom these days; it probably isn't exactly the same stuff that was used in the nineteenth century. At any rate, as I remember them, the plates have turned a mixture of dark brown and green, in quite a variety of shades. (The other metal-sheathed ships I've seen either have been drydocked - like the Cutty Sark and the Victory - or have had their plates painted - like the Constitution and Constellation. The latter came out of her latest restoration with her bottom painted bright green.)
The color probably varied depending on whether the ship was at sea or had been anchored for a lengthy period - and certainly would start to change rapidly if the ship were taken out of the water. In theory, I suppose, we ought to figure out just what we're trying to represent on a model. Do we want to show what it would look like at sea - with the surrounding water removed? Or have we lifted it out of the water, so the air can have its effect on the metal? In any case, given the nature and quantity of stuff that probably was stuck to the ship's bottom in real life, I'm not at all sure a literally accurate representation of it would be something I'd want in my living room.
Two of my models, pictures of which Michel was generous enough to post on his website ( www.hmsvictoryscalemodels.be/johntilleygallery.htm ) , show different approaches to the problem. The Bounty (which is known to have been coppered - though the designers of the Revell kit didn't know it) is plated with .001" copper sheets, applied to the plastic hull with contact cement. (It's now stuck quite firmly for about 28 years.) I painted it with Poly S acrylic hobby paint (no longer available, but PolyScale is close) in lots of shades of green, brown, and grey, applied "dry-brush" fashion in vertical strokes. I was trying to make the hull look as though it had spent considerable time in saltwater. If I were aiming for that effect on a plastic kit with a good representation of copper sheathing molded in, I'd probably paint it the same way. I wouldn't use copper paint; my personal opinion is that the metallic sheen would be gone from the surface after a short period.
The Phantom is based on the (no-longer-available) resin-hulled kit from Model Shipways. It came with a spool of (allegedly) copper foil tape with a pressure-sensitive adhesive on the back. It was twice as wide as it should have been, but after I cut it in half it worked quite nicely. I think the material is the same stuff used in stained glass windows. I don't know what's actually in it, but I suspect it is in fact copper that's been subjected to some sort of treatment that wards off the effects of oxidation. (Stained glass window makers don't want their copper to turn green.) I decided to see what would happen if I just applied it to the model and left it. So far (three or four years later), so good. It's gotten noticeably darker, but still looks metallic and shiny. I figure that's about what a freshly-coppered bottom would look like.
I'm afraid this ridiculously long post hasn't shed a great deal of light on the subject. The bottom line, I think, is that the treatment of a "copper" bottom leaves plenty of room for interpretation, guesswork, and personal taste - the sort of thing that makes this such an interesting and enjoyable hobby.