There are a few commercial "isoboxes" (didn't SoS review on a while ago?)but they are rather expensive and large! I would consider alternatives before embarking on any serious woodwork, smaller amp? Power soaks? Then, incarcerating a whole amplifier is difficult because of ventilation so I would suggest the first step would be to find or build a decent sounding 1x12" cab.
To be soundproof the box must be dense, MDF is the best bet, and airtight. Use XLR connectors not jacks. 3pin for the mic and 4pin for the speaker (or Speakon).
Such a box is a lot of work and not cheap even as a DIY proj' if you are to do a good job and use the right materials. Then, isoboxes are not it seems a complete answer and the alternatives I have mentioned might be at least as good sounding and more practical?
Checkout the "AxeTrak" site.