Yes, there are great public schools in Fort Worth. I don't know how familiar you are with the ranking system, but each school (unless it's too new) will have a ranking from the state based on a number of factors, including the assessment scores from student testing, drop-out rates, class size (student:teacher ratios), etc... Look for schools that are recognized and exemplary. Greatschools.org is a good website, which a lot of real estate agents do recommend. But, each school will have a website and posting of their ratings as well.
You said 'posting', so I wonder if a VA loan or Texas Veterans Land Board loan may be applicable in your situation. Great interest rates and service for qualified veterans. I'll post a website below that you may find helpful.
I do suggest you work with an agent. There are new areas of growth in Fort Worth that shouldn't be missed, and if you go it alone, you may grow weary of the search before you find them. There are lending programs in Fort Worth specific to certain zip codes that are for encouraging the sale of existing foreclosure and vacant short sale properties. For Fort Worth home purchases - new or resale, I recommend Paul Duncan from WR Starkey Mortgage. Ask Paul about the Fort Worth NSP.
Have a blessed day!