All items within this set of plans are built with 3/4" board. The type of wood is really not all that important. I generally use the cheapest I can find, so long as the wood is solid and without cracks.
It is extremely important to make sure all eight corners of each super are matched up before driving any nails. After glue is applied and the joints are slipped together, match up each corner one-by-one, and drive in the nail closest to the matched corner to hold it in place while you nail the remainder of the joint. This is especially necessary if working with slightly warped or cupped boards. With perfectly straight boards, there is generally no problem.
When nailing the top corners of the supers, be sure to place the corner nail down low enough so that it does not go into the rabbet joint instead of the wood itself.
Remember, it is always a good idea to use plenty of waterproof wood glue when assembling beekeeping equipment. It's better to use too much rather than too little (you can always wipe off the excess), so be generous!
The deep super and shallow super are put together with what I call a tab joint (really a modified box joint). It is nearly as strong as the finger joints used on commercially made equipment, but is much easier to make and requires no special tools.
It may appear at first glance that some of the dimensions are not called out in the plans. However, any that are not directly marked can be calculated from those that are.
Paint the equipment with exterior latex paint. I use white, though the color is not terribly important. A light-colored hive tends to stay cooler in summer. For as little paint as the equipment requires, I spend the extra money and get a pretty high quality paint. It pays me back in longevity of the equipment. Use at least two coats, preferably three or four.
You can shield the outer cover with some sort of sheet metal if you wish, but with adequate paint, this is optional.