An expensive one.
I'll assume you have a way to get GFCI electricity to the cabinet and that you are not putting it near a floor socket.
For this kind of display, you will definitely
need a sump that will let you keep all the ugly equipment out of sight (I think they are desirable in all cases but with a walk around it is pretty much a necessity). If you don't insist on corals or stay to very basic ones, octopuses and cuttlefish (another ceph you might consider) don't need any special lighting so any kind of ceiling light will help make the display attactive without causing the observer to need sun glasses. If you are going to want more intense light than putting it down close to the top would be easier on the eyes and more energy efficient.
A 55 gallon (65 for briareus) is the minimum gallonage recommened for most octopuses we typically keep and the bendensis cuttlefish. Ease of maintenance should be a primary consideration in designing the cabinet and you might consider doors on at least two sides. The tank needs to be large enough to accomodate a stand to hold the sump, any filtration you use (I use an 8" filter sock with charcoal and a skimmer and lots of water changes only). If you are pinched for space inside the cabinet, find an insump skimmer. The height of your cabinet will need to accomodate changing the skimmer collection cup and needs to be calculated into your design.
You can go very expensive with a round tank that looks great but will destroy your ability to take great photos. With cuttles this is a desirable shape to help prevent "but burn" when they get spooked. A rectangle should be much less expensive but doesn't have the cuttle advantage (some people baffle the corners for larger cuttles but the bandensis don't have a lot of problems with this) but photography is easier (reflection and back transparency will still limit the great shot). Corner cleaning is never fun and the rectangle is algae problematic when put together with silicone. You can get rectangles that only have one seam or you can look at acrylics that eliminate the silicone but still have hard to clean corners. Rounded corners help a lot and are easiter to get in acrylics (much more expensive than glass and internal scratching is a big problem. Forget what the vendors say about the fact that scratches can be buffed out. It takes a week of intense labor and an empty tank).
For an octopus, you will need a full top lid that can be tightly fastened down (not weighted, fastened). Depending upon the size of the tank, it will likely need at least one center support if you use a solid material. To keep heat down and ventilate the tank, some have used fiberglass screening as the cover but you will have to secure the perimeter. Duct tape has been the choice of many but I suspect latches are more in order here. I would suggest hinging it rather than requiring removal for weekly maintenance.
It is desirable in an octopus tank water level more than an inch below the top to help disuade escape. The deeper this air pocket the more it will help keep residue from building on the cover. We use a black band (different tanks have different materials) around the tops of our octo tanks to hide the water gap. If you are going to use a light hood rather than a ceiling fixture, this can be made deep enough to hide the lowered water level. We have used black acrylic bands around both the tops and the bottoms of some of our tanks for esthetics.
Hopefully this will get you thinking about the logistics and you can start a tank talk thread on how you might want to proceed.