Q:  Tells the operators one can override; which operators should he override?

A: Bottom line: don't puzzle your users.

Remember the reason of operator overloading: to decrease the cost and defect rate in code that uses your class. If you create operators which confuse users (because they're cool, because they make the code faster, since you have to prove to yourself that you can do it; doesn't really matter why), you've violated the entire reason for using operator overloading in the first place.