I would avoid Arlington, Irving, Duncanville and the surrounding areas as they are a bit older areas with less church presence and would be more dangerous than most northern DFW suburbs. If you are interested in the south side because of proximity to work, I'd recommend the south Forth Worth suburbs of Burleson, Mansfield, or Crowley. There are some nicer parts of Arlington, but you would need to do a lot of research to avoid the rough areas.

The Northeast Fort Worth suburbs are quite affluent and have strong wards and stakes. Flower Mound, Coppell, Southlake, and Keller all have excellent school districts but may be pricey. If you are looking for more affordable areas up there, I would recommend the Alliance area or Grapevine. Bedford is a bit older of a community but it is fairly central and has easy access to both Fort Worth And Dallas. North Richland Hills is similar. I'd avoid Hurst or Euless or Haltom City.

North Dallas is where most of the growth is happening. (Frisco, Prosper, Allen, McKinney and areas further north) The church is really strong up there, but there are some associated struggles. Traffic can be abysmal and the school districts are growing so fast that I don't know how working there would be for your wife. They are good schools and safe, but there might be overcrowded classrooms or lots of shifting schools as new ones open and taxes are outrageous to fund all of the new building.

If you are wanting a more small-town feel, you likely won't get that in any of the central suburbs, but there are some lovely towns on the outskirt areas. Azle, Midlothian, Waxahachie, Aledo, Argyle, Melissa are some examples. The east Dallas suburbs of Forney, Rockwall, and Wylie are very nice but traffic to Fort Worth would be awful.