Okay, great! I feel confident in recommending your advice: If you want an academic job and can find an adviser like this, go to grad school. Otherwise, do not go.

Of course, if everyone followed this advice I think you might be able to fit all the world's grad students in a high school classroom, because your adviser was freakishly good.

How does the funding work in the math department? Lots of the theorists I knew seemed to be TAs almost until the day they graduated -- and in their field, unlike the experimental sciences, salary seemed to be a major fraction of the expense of keeping a grad student. In the experimental wing, where it can cost hundreds of thousands of dollars a year to keep (e.g.) a genetics student stocked with reagents, the whole problem of adviser choice has an additional, frustrating degree of freedom: If your adviser doesn't have money to hire you, it doesn't matter that she's the greatest person in the world.

It might be possible to find someone who scores highly on the flush-with-cash axis, the graduates-students-on-time axis, the good-reputation-in-field axis, the track-record-of-successful-students axis and the provides-useful-research-advice axis... but such folks have their pick of grad student talent, and once they're done the other students have to pick among the remaining advisers, balancing the various factors and hoping to get lucky. Or, of course, they can quit, which is probably a better idea, though it is hard to make yourself do it once you've gone that far.

One overwhelmingly useful thing is to have independent funding. I had a fellowship and I cannot overstate how helpful it was -- I was able to shop for advisers in situations where my fellow students felt trapped by financial realities. If you find yourself headed for grad school, apply for every fellowship you can.