ooooooh, wood. I like wood.
There are really a couple ways to go about something like that. Best way is probably a single block of wood of whatever dimensions you like, then take a plunge router and rout out the inside, then round all the outside edges with a 1/4 round just to break off the edge a little. Only downside at all here would be the price. A solid block of appreciable size might be a little more than you would want to spend, and might be tough to find (if you don't know where to look)
The other really good choice would be to take a board, cut it into several sections of the right length, stack, glue, and clamp them, and then treat it as a single block. You'll see seam lines, but they may not be very noticable (depending on how you finish the wood, what kind of glue you use, etc).
The other alternative would be to just construct a box from standard stock, with all the board edges mitered at 45 degrees, that way all the seams are right at the edges. It would still look quite good, and you'd have options on look (maybe a maple box with a walnut top? or a light maple ans a cherry, or some other nice mix?) Probably the toughest to get right, but also one of the potentially better looking (depends on preference).
You should be able to get someone in your area to either make you one, or help you make one. Otherwise, I'd be willing to help you out.