We don't really have a 'regulation' bag. During new hire class you'll see a display in the training center lounge by Purdy Neat Things... those heavy black roller bags with the SWA logo on them as well as your name or monogram. I've had probably 5 of those bags. They have a long handle, so if you're tall, it's a comfortable pull. They're like $270.
Those bags are a little maintenance prone though. The 737-300 bag compartment in the cockpit is about a milimeter too small, so the side pockets tend to get snagged and the side zippers rip easily. Especially if there are any metal nubs or sharp ends in there.
The 737-700 cockpit is not a problem because it's a little bigger.
A lot of the FA's and I'm seeing more pilots now are using the Costco bag. It's like $70 and is warranteed for life.
I have both bags. The PNT bag is a little more useful and generally is stronger, except for the few shortcomings I mentioned. I'm having mine reconditioned and having them replace the thin zippers on the sides and pouches with the big heavy duty zippers on the main part of the bag.
Your bag will get dropped,dragged, piled on, stacked, trampled, sat upon, crushed, and generally abused. If I had to choose one over the other, the PNT bag with the logo would be the one. Just have something in reserve if you have to send yours in for mx.