First is that no education should take place on someone else's dime. Let the market sort it out. So don't subsidize literature or mathematics, film studies or nuclear engineering. Step back and let the market work it out.
The second is that the government should subsidize education, on the notion that some fields, such as science and engineering, generate positive externalities that can't be recouped by the practitioners of these fields. As you can probably tell, I think there's a lot of merit to this argument, especially in core science. I think that a scientist or engineer who earns 100K a year often generates far more wealth than, say, a mortgage broker who earns 100K a year. It does make sense to me that the government would try to find ways to encourage this.
If you feel this way, you probably don't mind educational subsidies and tax breaks for certain types of activities (by the way, I read somewhere that China has excepted software engineers from certain types of income taxes).
While I probably sound enthusiastic about this kind of arrangement, the truth is I'm ambivalent about it, largely because I have serious doubts that this kind of government interference will work. Instead, it often leads to a system that is easily gamed (engineering majors take the subsidy and then go work on wall street, and get a tax break because they write software for trading algorithms).
So in the end, I tend to favor a more hands-off, market based approach - though with some state subsidies for certain educational paths and research activity.
Lightweight yet effective and highly competent government... I do think it's possible, and the societies that figure it out will run circles around everyone else.