^This would be my joke answer, but I wouldn't mind if it were to become true; see below
In order:
Preferably an investor that doesn't have any kind of involvement in video games (but please, a good one, not another Index). That way, Atlus stays as it is.
If it is a third party, a Japanese one. Western working culture and Eastern traditions won't work well together. Which one, though, I don't know. GungHo... I don't know that much about them to give an honest opinion. Namco Bandai, I would fear for Atlus in the long run. Ideas?
If it is first party, Nintendo. I prefer to buy their hardware first, and after that whatever comes.