Here are what I regard, given my current information, as the best picks, alongside the ones Reagan chose for that position. They are not necessarily in order of strength because I don't know enough to do that.
She, according to a Philadelphia Inquirer article meant to be a hit piece, is "an ardent school choice advocate." The Inquirer adds, sarcastically, "Sorry, kids." Right, because not being able to choose a school is what's really good for kids.
Compare that to Terrel Bell, Reagan's choice. Reagan had said during the 1980 campaign that he wanted to get rid of the newly formed Department of Education. But he didn't try hard and his choice of Bell sent a signal that that wasn't about to happen.