This site advertises the octopus it sells as O. briareus, but the ones I got were O. hummelincki, and the ones others get that I've talked to have also been O. hummelincki.
Either way, O. hummelincki or O. briareus, or Abdopus aculeatus make good octopus pets. Again, I would request to get the smallest one available. Size isn't always a good way to tell age, but I'd rather get a dime-sized O. briareus knowing they grow to orange sized.
I personally like the look of the O. hummelincki best. It has the broadest variations in color and texture displays that I've seen and its proportions are balanced. O. briareus is pretty plain but has crazy long arms and webbing it stretches out over rocks. White/light blue with a sparkly green shine and red mottling, and not much in the way of texture. Abdopus is excellent with texture camouflage and has a few different color patterns.
Of those 3, O. briareus is a nocturnal species but can become accustomed to diurnal activity. It is also the only large-egged species of the 3, which means, the best suited for captive raised offspring.
Some advice for when you finally get one:
Use a critter keeper (plastic bug cage) to acclimate it in. Otherwise it will climb out of the bucket/box.
Try to feed it a thawed piece of food; raw shrimp, krill, silverside, etc. while it's acclimating. Offer the food on a stick, your hand may be too intimidating at first.
If it hides for a few days, let it hide. Do not go rummaging through the rockwork to find it. Imagine a giant hand coming in your house lifting up all the furniture looking for you. Would you come out?
Offer food on a stick. Move the food from one side of the tank to the other, wiggling it in cracks/crevices/holes in between rocks. Either you will eventually find it or it will be curious/hungry enough to come out on its own.
They sometimes like to dig. Make sure your rockwork is stable and sitting on the sand. Otherwise you may come home to a rockslide and a squished octopus, or a busted tank.
I think that's about it...