As mentioned upthread, the 2014 Impala is Chevy's new "big boat" car, and it's quite a good ride (but make sure you get one with the 3.6 V6... listed as 0-60mph in 6.8 seconds. The I-4 was a big sluggish in such a large car). Performs surprisingly well, though a touch mild-mannered. It's seriously my new favorite full/premium class vehicle.
I've also gotten uplevel Chargers, which are ok. The 300C definitely is a better car overall than its cousin, but I think the Ford Taurus beats the Chrysler offerings.
Something to consider... even though you booked into a premium, Avis will allow you to upgrade for a nominal upcharge (usually cheaper than if you just booked directly into a higher class). If you don't mind cost, I would recommend a Cadillac XTS as a nice American road yacht (I don't much prefer Ford products, which Lincolns are).
Personally, if you want a real American driving experience, I would opt for a Chevy Suburban/GMC Yukon XL (LTZ/Denali trims respectively for the top-level features). Nothing like 2.5 tons of metal rumbling down the freeway, driven by a V-8, just to haul you and some luggage around. Lots of room the spread out. Better yet... I've seen Chevy Silverados (full-size pickup trucks) starting to appear on the lot.
At LAX outside of the Preferred booth (shuttle bus drops you off in front), there will be an "Exchange" aisle of cars (on the other side of the bus) where you can just pick any car parked there, though most of the time those are of the Intermediate class and up. There will also be an "Upgrade" area. Also feel free to walk the lot and note the stall number of any car that you may want to switch into.
Finally, some random words of advice for your trip:
- Get a lighter color car... the Arizona heat will bake you in a dark car.
- Get a lighter color interior for the same reason as above... but this may be more limited.
- Get a car with remote start, so you can cool down your cabin before getting in (FYI the XTS and Suburban/Yukon have cooling seats).
- Get a car with XM activated, so you have uninterrupted audio stations on your trek.