I'm flying Delta. My brother flew the same route a few months ago with no problems. And despite their financial woes, they have a fair safety record. With the exception of sites like Hotwire, you can usually see what airline it is before you book the flight.
If you're looking at round-trip, your return date is also going to have an effect on your fare.
I don't normally use Travelocity, Expedia, or Yahoo Travel because I've had better luck with other sites. But that may be because of where and when I fly... I'm also pretty flexible about what airline I fly, number of layovers, etc.