What good do models do you? Most rental car companies in the US only let you reserve a car category, not a specific model (especially if you're limited "up to standard"). Now, with Avis or Hertz status you may be able Exchange (that's the Avis term) for another car form a limited selection in the lot, but again that selection will have random cars in a few different categories. At some Avis lots in the US I find 8 cars, once I found only 1 car, in the Exchange area! There'a also often an upgrade area; are you allowed to pay to upgrade a car at the lot?

So IMHO you need to have a big list of ranked cars and then expect to find only a random small subset of those available to you at arrival time at any particular location.

And btw don't assume just American cars. At Hertz and Avis in the US I keep getting Kia, Toyota, Huyndai, Nissan, etc, and only occasionally an American brand car.