In Vedic Astrology, Budha represents speech and communication, skills, intellect, dexterity, equanimity, neutrality, curiosity, playfulness.
Strengthening Mercury with a gemstone usually affects the mind first. Mercury relates to mental processing, communication, and speech. It also affects wit, sharpness, intellect, and quickness.
Emerald is the gemstone for Mercury. Curiously, like the human mind, an emerald is never completely flawless. Emerald color also cannot be accurately photographed and we suspect this is because it is a color interpreted very specifically by the mind.
Green tourmaline is also a great gem for Mercury. Peridot is the third choice.