Do yourself a favor use AT least 3/4" mdf and before you close it all up.. get some mdf sealer.. its a spray and it will cover the mdf with a glue type substance which will also allow for less air leakage. If you have access to a air nailer use that to nail your box togeter or if you don't use screws and glue it as well as nail/screw it. The less air coming out of a box the better. And yes those dimensions you came up with our the inside size., so like you said take in accoun the 3/4" of that as well.