My '97 accord specs some kind of type SH oil, but I can't find any such thing anywhere. What does that mean anyway?

Good luck finding that one (what they list in the manual.) Really, as long as it meets the grade for SH (it should say on the back of the bottle, in the circle where it also states "Energy Conserving") it should be fine. I personally use Castrol Syntec Blend, 5w30.