i think Nancy's list is right on, however there's a LOT of wives' tails regarding keeping octos. I had a California 2-spot that i found here in local waters, in my 73-degree water w/ the smallest chiller money can buy, and he did fine (and was old/large when i found him). i think that, like a lot of organisms, they adapt. and, if you consider that in the wild in a place like SoCal, they're in water with a HUGE range of temperatures - colder, deeper areas around 58-64 degrees, then in smaller, warmer pools of water like when i found mine. There was BARELY any water and he was under a rock...the water felt like 78 degrees at the coolest! i was amazed he wasn't dead...but like i said, they adapt to whatever pool of water they're in.
also, people say you need a huge amount of water which isn't entirely proven. At the Cabrillo Aquarium in San Pedro, CA, i visit a 7 year old 2-spot Bimac which is HUGE! Its mantle is about the size of a squash with very long arms, and they have her in a 60 gallon tank. so, nowhere does it say an octo needs a ton of water to survive. Just look at the very little amount of water that are in tidepools that they love to hang out in.
i think overall the saltwater hobby tends to push people into buying a lot of unnecessary stuff. there's a guy in KoreanTown (LA) who actually has LIVE, HEALTHY saltwater fish in systems with NO filtration systems...only aerators...unreal, i know, but....he swears by it and he's a wise, 80 year old Japanese fellow...interesting stuff though, either way!