I only shoot through plastic when I absolutely must, when the coin is in a slab from which I don't want to crack it. Otherwise, the plastic introduces additional difficulties, especially non-rigid cellophane which rarely stays flat or parallel to the coin, that makes things a whole lot more difficult. You're increasing the problems to overcome drastically by not shooting the coins raw.
If you must, use a diffusing technique similar to what triggersmob describes, to avoid dirrect glare from the plastic. I'd advise artificial light under all circumstances - natural sunlight is merciless on a coin. Learn your camera's White Balance functions. If it has the ability to set a Custom white balance, use it. Color is tough to adjust after the fact, and if you can get it right in the camera you'll be saving yourself a lot of work. If your camera has a good Custom white balance, your choice of lighting gets a whole lot easier.
Beyond that, every camera is somewhat different regarding what works best. You'll need to figure out what distance to keep the camera from the coin, and what settings it likes best. Generally, try to keep your exposures as short as possible, never less than 1/100, even if it means setting ISO to 400. Use the smallest numerical aperture that will keep the whole coin in focus, because the wider (smaller numerically) the aperture, the shorter your exposure can be. Longer exposures lead to less-sharp focus.
I shoot on whatever background appeals to me at the moment. Generally, the more silver or lustrous the coin, the darker the background wants to be. Copper, color and duller coins like lighter backgrounds. Grey is an excellent all-around compromise.