There are many different types of wood you could buy to make a giant jenga set. The cheapest though would be just standard 2x4's from your local hardware store, probably come in lengths of 8 feet.
You need 54 pieces to probably stack the blocks. If each block is a foot long, then you would need 7 - 2"x4"'s that are 8' long. The easist way to cut would be to use a miter saw, so you can set the exact length each time. If using a manual saw, then your edges might not be even, but it would still work.
After you have all your pieces, it would help to sand them down to make the smooth to slide in and out. Once sanded remember to wipe them down or else the sawdust will cuase friction and make it harder to slide them out.