Buy a house or pay off student loans?

I'm new here so sorry if I post this in the wrong area. I recently inherited property in KY and because I am a Class C inheritor I will have to pay an inheritance tax. I plan on selling the property, and I'm looking at having about $150K in cash after taxes and all of the estate bills are paid and settled. Initially I wanted to take the money and buy a house. My wife and I rent a 3 bedroom apartment for $700 a month, plus about $75+/- for water and $150+/- for electricity. We have a 3 bedroom for us, our 3 month old, and my wife's grandma who provides child care during the day to save money. The dilemma we are both having is whether we should buy a house, or pay off our student loan debt. Together we have about 110K in student loans, which totals to about $700 a month. My loan is fairly low, so if the debt is forgiven after 10 years I will have paid about $18K instead of the $51K that I initially borrowed. I'm unsure on what my wife will have paid after 10 years. Which would be better, buying a house or paying off the loans? I like the idea of buying a house without taking out another loan, so I'm leaning in that direction already.