Avis through BA are fine. It’s typically fully inclusive with no excess. One way rentals are almost always free within CA, NV and AZ as a tri-state region, with any of the larger companies. Through BA all that’s typically missing is roadside assistance and personal accident stuff, both of which are optional, and personally I never bother with. If you’ve done the booking as far as pricing then the insurance details are there to read.
I’d say Avis and Hertz much of a much, and I’d prefer either of these to Thrifty or Alamo. I’m sure if you rent cars enough you’ll have your own problem stories eventually. I’ve yet to have a problem that wasn’t resolved by being patient and calmly demanding.