I would also say AA, except a key question will be - are the non-stop AA flights really the cheapest? Or will your company be pushing you to connect on cheaper flights anyway?

Theoretically, a case could be made to just connect at IAH on Continental. Especially if you want to qualify for elite status using segments.

Can you run some hypothetical scenarios and see which airline the company's policies would lead you toward? And how status may or may not matter to you?

I'd try to avoid Southwest if award redemption is important to you. If all you're buying is cheap "Wanna Get Away" fares, you may dramatically reduce your earning rate compared to a scenario where you are connecting on an airline with 500-mile minimums and elite status bonuses.

Tho it is nice to always fly on a full-sized plane.