I'm playing the Secret of the Silver Blades and attempting to gather all the pieces of the Staff of Oswulf. Upon finding a piece on the 5th level of the mines, I also found a Stone of Good Luck. My question is what is this artifact ,what does it do, and which type of character (fighter, cleric, thief, mage) should I give it to?

In the AD&D tabletop rules, a Stone of Good Luck gives the character a +1 bonus to his saving throws. So likely this how it is implemented in the game.