Buying a first house, what will I likely be approved for?

[Aaron Hollenbach]

Hey Everyone! My Fiancé and I are looking to purchase our first house shortly after our wedding in June of next year. We are pretty confused as to everything that goes into buying a first home, and what we can afford. We both have fairly extensive student loan debts with a total of around $220,000. Below I will list what I think are all the main elements that are relevant to buying a house. 

My Info: Annual income ~$80,000 My Credit Score: ~680

Fiancé Info: Annual Income : $60,000 Fiancé Credit Score: ~740

Down payment : $15,000

Debts:

Monthly Student Loan Payment: $2000 + $500 extra

Monthly Car Payments: $600

Total Monthly Payments: $3100

From my understanding this puts my pre-mortgage DTI at ~27%

What are we likely to be approved for?

Most of the houses we are looking into are within the $275,000 - $375,000 range. Are these feasible?