We have unsuccessfully attempted a number of ways to come up with practical guidelines for both volume and shape. A lot depends upon the octopus (species, sex and individuals). Some species are more active than others and need swimming and multiple den areas. Some (like the female mercatoris) tend to pick a den and and rarely leave. You will see many reports from the academic world of escapes but they are actually quite rare in our journals (quite possibly because we emphasize good fitting tops and latches). Some species have very long arms so height is a consideration in addition to width. So trying to generalize just has not worked. I will say from personal experience that a too small tank almost always leads to multiple escape attempts. Where this is more water quality or size (I believe it is size) is not wholly clear. I wish I could be less vague. I tend to keep more than one octopus at a time and have multiple tanks that are suitable. If one starts outgrowing its tank, I usually have somewhere else to move it to but not everyone has this luxury.
The belief that an octo will kill ANYTHING in its tank is over stated. HOWEVER, what you put in the tank matters. Be sure to read the
It Works Until It Doesn't experience article that CaptFish wrote about his briareus. You will read (mostly in other forums) that some fish do just fine with an octopus. What you don't read, and why Dave wrote the article is what happens after they post their stories about the octo buddies. I simply say, NO FISH. That being said, there are other animals that do survive well with all octopuses and some that will do well with most octopuses (caveate, some of these only do well once the animal is established but may be eaten the first couple of weeks until it finds that it is being given more desireable food regularly).
Somewhere I have given multiple lists of animals I keep but I will relist the ones I can think of here.
Serpent stars
Brittle stars (avoid the greens)
Thorney stars (Caribbean, day active and often very brightly colored and hardy - in spite of what I have seen on the net and they definitely eat meat - but they need a well established tank)
Pencil urchins (other have been successful with pin cushion urchins but I have not tried them)
Gorgonians (best added after your tank is well established, placed in a relatively high flow area and away from normal open hunting ground - octos do not go around things)
Leather corals (again, placed where they won't get trampled and after the tank is well established)
Mushrooms (but not ricordia or anemones)
SOME polyps (secure to a separate rock, if the octo reacts remove them)
Snails (may be eaten, especially when the animal is first introduced - only my vulgaris ate these after introduction but others have used them for food much longer)
Hermit crabs (may be eaten, especially when the animal is first introduced - only my vulgaris ate these after introduction but others have used them for food much longer)
Macro algae (the most decorative don't seem to live long though but they are good for a tank and replacement as they dye has no negative impact. Be careful about your choice though some can take over a tank).
Marine tanks are quite different from freshwater tanks and my best advice is to build out your tank over a year's time before adding an octopus. An experienced keeper will build the bacteria over a 3 month period or, using existing substrate might shorten that time if moving from a smaller to a larger tank but there is a lot to learn about keeping a saltwater tank and a lot of habits that need to be acquired. Many people will cycle the tank with fish, I don't recommend this method but it does work. Removing the fish will be disruptive to the tank and then you must find somewhere to house them.
Be aware that your LSF will tell you your tank is cycled when your ammonia and nitrites spike and then go to zero (often after the first month or so). This is just the beginning. At that point you will need to build the bacteria to levels that support a very messy eater. Putting too many animals in a newly cycled tank and killing most everything has a name. Look up
New Tank Syndrome.
You can use your sump for feeder animals but it will paritially defeat the advantage of extra volume (but not the convenience and safety of having equipment remote from the octopus) since you will have to feed them and will have detritus from both the animals and the uneaten food. I prefer to keep a couple of small, inexpensive tanks around. some people will combine a sump with a refugium to grow macro algae and small food critters. The macro algae helps to reduce the nitrates but requires lighting and additional care and space. My personal preference is to use the sump only for filtration equipment and extra water volume. Keep in mind that your sump will not be filled as you will have to allow for the drain off water from the main tank when the power is off. This will be several gallons but depends upon your tank configuration.