For me it depends upon the circumstances and to some extent the audience of players. So I voted for "other." For some settings and rulesets, unless the PCs are very green, such identification doesn't present much of a challenge. So I'd roll with the 2nd choice. In other settings however, the knowledge and skill to identify gems can be a rare talent. In that case I'd begin at option 3, giving the least details and allowing players to RP through the process of IDing them.
My players are going to have some influence too, in that some players just aren't that keen on the RP of IDing and evaluating of items like gems. For such players I might just do a handwaving of it, by giving the most details. I certainly have a few cicrle of players that really like to do a full geek on such RP. And of course there's those rare gems, who's IDing IMO shouldn't be handwaved. If only because doing so can eliminate the potential for good narrative, RPing and maybe even plot hooks.