The fact that he oversyed his visa will not effect his application if he is marrying a US citizen. However, if under hte J visa he was subject to hte 2 year home residency requirement he may have to apply for a waiver.
Your wife can be denied a green card if you do not meet the poverty guidelines for income. You can get a joint sponsor who is a citizen or permanent resident that does earn sufficient income to joint sponsor her. Once the 485 is filed she will not have to continue going to school. Consult an experienced immigration attorney.