FHA is generally a bit on the expensive side for someone with a 750 score. FHA doesn't credit score, so if you have weak credit, it's fantastic, and sorely underutilized.
With FHA, you have to pay a 1.5% upfront mortgage insurance premium, which is almost always financed into the loan. You have to put 3% into the transaction, with at minimum 2.25% as actual downpayment. After that, you also pay .5% annually for ongoing mortgage insurance.
Worst part of that, FHA only allows you to drop the monthly MI after you've paid your balance down to 78% of the original purchase price value of the home. You cannot get a new appraisal and use the appreciation to drop mortgage insurance, like you can with a conventional loan. Conventional loans, typically have to wait 2 years to get a new appraisal, but after that, if the home jumped up in value, MI can be dropped.
So ultimately, FHA would likely cost you more. Your loan officers should be very able and willing to give you a 5 or 10 year cost breakdown for both.
Some mortgage companies have cheaper mortgage insurance rates than others too, at least with 5% down or more. Ask about their coverage levels. Shop that part too. It can save you almost a quarter-point annually.
10 years in mortgage banking