Well, there's nothing *really* canonical about it... we're all just spitballing here.
There does seem to be some fanboy consensus that Luthor should be #1, 'cause that's his schtick. If he's not the biggest brain around, he's severely diminished as Superman's arch-villain.
For a long time Mr. Terrific was definitionally "the third smartest person in the world." Personally, I thought this was a wonderful bit of fan trolling, because it allowed for endless debates about who could be #2 (Batman? Sivana? A genius we've never heard of?) Recently, however, it's been implied (in the Adam Strange series, I think) that Terrific only says that to be polite - so he may actually be #2.
Once you get past the first two or three, I think it's all just silly (but fun) fanboy conjecture.
For my money:
- Ray Palmer is the go-to heroic scientist when you want something explained/figured without a lot of baggage. He's a low-grade Reed Richards, without the skills to reimagine an entire scientific field over lunch.
- John Henry Irons is the guy you go to when you want a machine built that no one has ever built before.
- Niles Caulder is who you consult about insane fringe fields of scientific discovery. And then you cross check all his theories with Palmer, 'cause Caulder arguably insane.
- Will Magnus is who you bring in for robotics. Duh.
- Barbara Gordon is the point person for all things computer (or John Marshall... but everyone's forgotten about him).
- Although Batman is up-to-date on everything (and can cross-check everyone's math), he's mostly wasted in the lab.