Also what is important to communicate to a buyer is that although the asking price may be $100k, if the comps show it may be worth $140k you will need to offer "more" than the asking price and no more than 3% for closing costs.
Lastly, owner-occupants have first chance at Fannie Mae owned properties so you may want to show those properties first.
Just let them know you will be working for them and continue to show them other properties to keep them interested while you are waiting on a response from the bank.
Banks like the highest price but they also like a confident buyer. Put a larger earnest deposit down.
You also want to work with a lender that understands this process and can assist you in comforting the buyer and keeping them on board.