Underwriters like to see income stable or increasing.
As far as the student loan, your required monthly payment on that will be considered into your debt ratio and that could reduce the amount you qualify for. If you are delinquent on the student loan that would disqualify you. Having an approved deferment, though, is okay.
The monthly amount that you will have to pay after the deferment ends will still be figured into your debt ratio.
On a related matter, investigate buying flood, wind and hurricane insurance. Homeowners in Brick suffered millions of dollars of flood damage from hurricane Sandy. Those without flood insurance suffered considerable economic loss. Many of those people had to get long term, low interest loans on top of the mortgage they already had, to repair their damages.
I think doing this in person is very important for a first time home buyer.
Good luck on your home search.