Tennant Prospects

[Matt Turner]

My house has been on the market for almost 4 days now.  i have had a ton of phone calls and multiple people come by that qualify and would be great.  one couple i am talking to has a husband that is in the air force.  They are wondering if i could let them sign a lease starting in June but not move in until August, but pay half the rent for June and July.  Being a pilot in the air force catches my eye for good renters.  

what should i do about this?  should i even be looking into this?  should i consider it and bump the price up from 1150/ month to 1200/ month to make up for the lost amount.

I have not done a background check yet with these people.