Studying photos of the real thing is, of course, an excellent idea - but take everything you see with a large grain of salt. The people responsible for restoring and maintaining the Constitution know what they're doing, but they have to take all sorts of things other than authenticity into consideration. She's no longer a warship; she's a tourist attraction. That fact has all sorts of implications in terms of her upkeep and appearance.
The deck planking of that ship has been replaced several times since she was built, and I'm pretty sure the current stuff bears little resemblance to the original. On another website not too long ago somebody posted some pictures he'd taken on board her. It was pretty clear that a considerable area of the spar deck near the mainmast had been painted black. (I can't imagine why, but I imagine there was a good reason.) There's just no way that was the case during the War of 1812.
We had a discussion in another thread recently about deck colors for sailing ships. My own opinion, for what little it's worth, is that there's plenty of room in subjects like this for artistic license and personal taste. But it's always a good idea, I think, to start out (if possible) with an understanding of what the real thing looked like.
If I'm not mistaken, the Constitution's original deck planking was either pine or fir. When freshly cut, both of those woods are a pale, greyish beige with a slight yellowish tinge. Generally speaking the planking was left unfinished; it didn't get any oil or varnish. (The idea was to provide an un-slippery footing for the hundreds of men who had to walk on it.) The daily maintenance routine during the ship's active service included "holystoning" - scrubbing the planking with salt water and blocks of pumice ("holystones"). And of course it would be subjected constantly to rain, salt water, sunlight, and the pressure of shoes and bare feet.
Historical novels are fond of referring to the "snow white decks" of sailing warships. I have my doubts about how "white" they actually were; I've never seen a bare wood deck myself that could reasonably be described as white, and marine artists rarely if ever show them that way. My personal taste runs toward a pale grey with a hint of beige. (The background color for these Forum pages is, to my notion, in the right neighborhood, though a trifle dark) For wood decks I like to use holly (which is almost pure white, and has a wonderfully fine grain that actually looks like miniature wood), with a very light coat of "Driftwood" colored stain. For painting plastic to look like deck planking, I like a color in the PolyScale acrylic hobby paint range called "weathered concrete."
Hope that helps a little. But don't leave your own ideas and taste out of the picture.