Stone, Clinton lied under oath during an official investigation...in short, he perjured himself. That is a specific crime defined by a specific statute...I would suggest that makes the case against him a great deal more supportable.
I agree that bringing the charge was entirely within the House's authority, simply because they have essentially unlimited authority to do so under the 'High Crimes and Misdemeanors' statement in the Constitution. I would consider it to be a misdemeanor, but not necessarily a High Misdemeanor: i.e, a misdemeanor that significantly harmed--or even potentionally harmed--the State.
It should be noted that there is precedence for using practically any misdemeanor to bring impeachment charges. In all such cases, however, the impeachment charges were not upheld by the Senate.
I can envision circumstances where impeachment charges should be made even though no statute had been violated and should be upheld by the Senate. For instance, if the VP repeatedly appeared before Congress while drunk and using vile language. This would definitely be a high misdemeanor as it would be damaging to the reputation of the country.