I never use discounters. I manage all the air travel for our family and my husband with our business.
I only use the American Airlines site for airfare or Southwest Airlines.
SW has some fantastic deals if you look. My hubby has to fly to Houston often and I get him down there for $112 round trip, routinely when they have an airfare sale. I book in advance because we know he is going. There are more rules with the special fares such as no changes, etc. HOWEVER, if for some reason you can't go and you don't use the ticket, as long as you call te airline ahead of time, you do not lose the $$, it stays in a credit for your next flight for a year.
We use American for many flights as well. We prefer non-stops but you can manage a better fare sometimes if you do take a layover or change planes.
It is easy to get to CA from TX, it just takes a little planning and research.
As for the discounters.... they are not going to take care of you if something goes wrong. You get what you pay for.