Hello my fellow Texan!
Based on the below scenario, you have several viable options available to you. But drilling down on your FHA request and based on the numbers provided, here's my take:
(H) Estimated PITI - $1,850.00 (Not quoting this is an actual payment based on a sales price, just an approximation to keep your DTI from being too high)
(I) Total Gross Monthly Income - $7,208.00
(D) Total Monthly Debt - $2,028.00
H divided by I = 25%
H + D divided by I = 53%
Summary: With the scenario you listed to include a credit score above 620, I can am pretty sure that the AUS (automated underwriting system) under the FHA Scorecard will approve you even with a 53% DTI. I was working on a loan for an borrower this morning with a median credit score less than yous, several collections, and was still able to get an AUS Approve/Eligible with a 56% DTI. My recommendation would be to try and save as much money as you can over the next few months and then start the process no later than May. I would make sure whoever you work with is an experienced Loan Officer who will run your loan application through the AUS and will to share the Findings with you. This way you can see upfront what conditions you will need to satisfy. Be mindful that there are lenders to include my company that underwrite directly off the DU Findings. Make sure you don't find yourself working with a lender that has additional overlays (extra layers of internal guidelines or restrictions). Hopefully this illustration will assist you.
Best wishes to you and...
Based on the info you've provided, you should be good up to $220,000 +/- depending on the property taxes & whether or not you'll have to pay HOAs or flood insurance.
One big caveat here is this: If you are married & your spouse is not going to be on the loan, lenders will still have to count her debt against your income on an FHA, VA* or USDA loan. Depending on the amount of debt your spouse has, you may have to go with a conventional loan, add your spouse to the loan or pay off some debt.
A conventional loan will limit your DTI to 50% with a 700 score so you'll need to pick up at least 8 points on your mid score if you have to go this route.
Depending on where you're buying in Texas, you could have lower taxes which will help as well.
*VA has an option that allows us to get around this issue.