I would recommend, in this order:
1. Save up for, or, if you already have, keep an emergency fund. Lack of emergency funds is what tends to throw people off course on their savings/payoff plans, and put them further into debt.
2. Pay off the student loans. I understand the desire to purchase a home, but I think it would be better to at least get the student loan debt down quite a bit before going into a mortage, property taxes, homeowners insurance, and the cost of maintaining and repairing a home. Additionally, I think it might be stretching yourself thin to have a new marriage, a new home, graduate school, and a full time job all at the same time.
3. Save up enough that you can not only purchase the home, but still have your emergency funds untouched as well as budgeting for the "hidden costs" of owning a home, to avoid credit card debt when (not if) something goes wrong with the home.