This post is not a very answer-able one. There are a wide range that would do fine in captivity, however only a few species are typically available. Carol doesn't know for sure the species of her octo, I believe she is leaning toward
O. Vulgaris, due to his large size. I think Vulgaris is right to through the pictures I saw. I think that because he looked a lot like the
O. Humellincki I had for a little bit, minus the eyespots. People used to think Vulgaris and Humellincki (wish they would change it back to Filosus ^^

were the same species , so it makes sense (to me, at least) that Biddle would be Vulgaris. He very well could be another species as well.
The most common octopus to be kept is
O. Bimaculoides, or a Bimac. The vast majority of this species is outgoing, playful, energetic, medium-sized, and fairly easy to take care of. Another plus is they are diurnal. The downside of this species is they are from cold water (60-72 fahrenheit is ideal), and it could be hard to keep the temp where it should be. These are also the most common (pretty much only purposefully) octopus to be captive bred at the moment.
I'm not about to give a profile on several octopuses that are good for captivity (although I might if I was bored and hyper... of which I am only the first

) but I will give you some species names that usually do well, and you can research them on your own... Here we go:
(genus of all should be Octopus, although some may fall into another odd [closely-related] one)
Cyanea
Humellincki or Filosus (Tonmoers that have kept this species find it to be perfect, but they always seem to mysteriously die)
Vulgaris (big tank)
Aculeatus
Briareus
Mercatoris (dwarf therefore nocturnal, small, and shorter lived than larger ones)
Joubini (see Mercatoris)
There are a bunch more that people'll get every once in a while. Most aren't properly identified until you get them and notice their behavior and pattern.
Hope I helped
Good luck