I grew up in the Protestant tradition but have recently been baptized in the Catholic faith. My wife, however, is still Protestant and we like the church we go to on Sunday mornings, but we also want to go to Mass. Can I go to Mass on a weekday or a Saturday?
You can go to a weekday Mass whenever you wish. But if you are referring to fulfilling your Sunday obligation, that can only be done on Sunday or at the Saturday evening vigil Mass. I would caution you though that attendance at a Protestant church should be an occasional thing. Regularly attending Protestant services, particularly when you are so new to the Catholic faith, can dilute your Catholic commitment.