No smaller than a 20 gallon, preferably 30 gallon (less water quality issues). You won't need a light for daytime viewing, they don't come out until it's dark. Red lighting helps.
I had one for 4 months. I saw it outside its den rarely, and for only a few moments. They seem to appreciate having things to interact with. I kept mine inside a critter keeper with some live rock and shells, inside a community tank. The octopus would approach or at least reach out to fish swimming near the critter keeper. I moved it to a 10 gallon by itself and it NEVER left its den for almost a month. Moved it back to the community tank, started coming out again. Others who keep multiples together seem to get a lot more action out of them than I did. That's speaking of this species only though.
Honestly I'd recommend just biting the bullet and getting a bigger tank for a bigger species. Most of the mid-sized octos are very personable once they "get to know you". A 55 gallon would do for an Abdopus or an O. hummellincki. I've found the more space they have the more variety of behavior you'll see. Sand zone, rock zone, open swimming space in the water column.