Check your local information place (phone book, in the USA) for "Lumberyards" or "Lumber". The lumberyard can and will get you the piece you desire. It is their business! Some may not cut to your dimensions, so remember that when searching around. Your sweet honey-like tone will go a long way towards getting what you want from someone you've never dealt with.
If you want/need something exotic, go to
Rockler and you'll be able to get something that thick. Be prepared to reach through your nose to access your wallet, as that's how expensive their wood is.
If you want cheap, and are thinking plywood, MDF, or some other sheet-good, you can do it easier than you think. A little Gorilla glue, a few clamps, and a few cauls (ask me if you go this route, I'll explain what a caul is and why you SHOULD use one) and you're in bidness! It's not as hard as you might be envisioning, and you won't even require screws in it.