I think a universal answer cannot be given. Too many things affect the decision that you haven't mentioned: first of all, are you developing a library or an application?
In the first case, flexibility should be favored and the best choice is usually to design your interface in a way that leaves the decision up to the client. Since you don't know what clients will use your class and which requirements they will have, it's best to make as few assumptions as possible. If your clients have tight performance requirements, they won't be willing to pay the performance penalty of an extra bounds check, for instance. This is, basically, the reason why bound checks are not performed by STL either.
In the second case, it depends on the performance requirements of your application and the exception safety guarantees your class has to provide. Which operations need to be no-throw? Are you allowing or planning to use your class inside an STL container? Is it going to be used in the most critical part of your application, so that a small performance performance gain in the algorithms of this class will affect the overall execution time of your application?
There is no such a thing as a "universally best design". Engineering is all about finding the right compromise according to the particular situation at hand, and software engineering is no exception to this.