Use MDF or Baltic Birch plywood. You can veneer the cabinet with any sort of real wood you prefer. But you want a composite wood product like MDF or plywood because solid woods have natural resonances that you want to avoid. Also, when using plywood, make sure to use only Baltic Birch because it is void-free. Cheaper plywoods have voids, and the debris in the void will buzz when the speaker is used.
Sorry to butt in on your question, Reinhardt, but I'm curious about something. Would OSB be an okay alternative? I have so much of it around my house and I'd love to use it for something. I would want to sand it down some though, for aesthetic purposes, so I don't know if it would still be thick enough to use for this purpose. Is that something I need to keep in mind?