I don't think it matters too much how you build your box, personally I just went with a square frame design like you would use for building a deck, with beams inbetween for support and then a layer of plywood on top and then the HDPE screwed in on top of that using a countersink drill bit and galvanized screws. I've seen other people use really ghetto designs and they seem to hold up fine. It's more important that you use good materials rather than you know anything at all about carpentry.
If you plan on leaving it outside however, do not make my mistake and use untreated plywood. Mine warped all over the place and I'm going to have to resurface it. The normal untreated 2x4's painted with a wood sealant are fine however and remain unwarped.