There are two components to consider.....
1) Can you get a loan?
2) What is your comfort level with the financial obligations you will take on? Some people intentionally purchase below the threshold for which they qualify, especially if they foresee instability in their future work or income. Are yo in any type of step-up program in your job? If so, you may be more comfortable borrowing at the maximum for which you qualify.
With an FHA loan, you will need 3.5% down, plus closing costs. You can make an offer to purchase and ask a seller to pay part of your closing costs for you, which will decrease the amount of cash funds you need to make the purchase. Be aware that when a seller pays closing costs, a property must meet an appraisal value which will include those contributions. Your Realtor and loan officer will help you understand that in detail. Herein, I simply wanted to give you the basic starting info from which you can explore further.
Here is a link for several mortgage calculators. These can be quite helpful and educational, but won't take the place of meeting w/ a mortgage professional. Most buyers tell me these are quite helpful to them as a precursor to meeting w/ a mortgage rep. It helps them better understand the discussions with mortgage reps and increases their confidence.
When speaking w/ a loan officer, inquire if they have any special programs for individuals in law enforcement. I don't know if this type of program exists in AL, but it does in some other states. Not all loan officers have access to them, so you will need to ask around.
All the best,