My starter home was in the Cultural District area of Fort Worth. That was in 2012, and I'd guess it may not be too cheap anymore, even for smaller houses (mostly under 2000 sq ft). If you're single, it is a great place though. Just enough house for yourself, close to social activities, and right off I-30. Do not envy that commute to Arlington though...
I feel like Benbrook is also slept on a bit. A lot more affordable options, easy access to I-20, and close enough to Fort Worth. But, a terrible commute to the ballpark.
HEB area is also pretty decent. Decent home prices and close proximity to everything. Probably not too much further than where you are right now. You might can take 157 all the way and avoid the highways. The area along 121 between Cheek-Sparger and Glade has blown up the last few years...a lot of restaurants, shops, etc...Plus, very close to DFW is that's of any importance (and not very far to DAL either).
Keller is going to be a beastly commute, and it is pretty suburban. Mansfield would bore me if I were single. But, not a bad place for a starter home.