HUD has a "Good Neighbor Next Door" program that affords law enforcement/EMT/Teachers/etc to purchase houses for less than half the market value in designated neighborhoods.
Check with a credit union in your area or one recommended by the Fraternal Order of Police, Sheriffs Association, etc. Ask your fellow officers, as special mortgages aren't usually adverised.
As far as mortagages, the possibilities are endless. Luckily, special ones that cater to law enforcement are available. You can simply do a google search online and many different ones will pop up.