Certified Pre-owned from the manufacturer dealer is often the best way to go.

For AWD cars, look at Subaru.

Any reason your are not considering a Truck?

Fuel economy and price. I imagine trucks are more expensive than compact SUVs, am I right?

Now I'm a homeowner almost daily I wish I had bought a truck.

Still considering a couple thousand beater truck for odd jobs.

She's a he, as you well know

As for the last part, how well you know me!

<waves back> <blows kisses>

You're right though. A lot of Americans aren't very good drivers. Namely teenagers, women and Asians. And Mexicans. And Texans. And Wyomingans.

My first job in this country was a salesman for the main Ford dealer in our area. I did learn this .... You will need to obtain a US driving licence to lease or buy a new car, your UK licence will not be valid after 30 days anyway.
As for the credit history ... A car loan is the fastest and easiest way to build up your credit, most banks will lend you money for a car if you put a lump sum down.

That's not true in most states.
That is only true in some states, it varies between 10 days and 90 days depending on the state, and PA allows new immigrants 365 days.

So, do I need to have first the SSN card and the state driver's license to buy a car with cash and to set up insurance for that car?
Or can I do both before having the SSN?

I plan to get the driver's license as soon as possible, but, according to the Idaho DMV requirements, to apply I need first to get the SSN card and a proof of address.

And get a decent warranty. We probably overpaid for the car but got a "free" warranty that subsequent dealerships said was pretty comprehensive. Anyway, long story short, well over $2k of labour and car rentals charged to the warranty people to replace a $5 part cost us $50 in co-pays. They basically had to take everything out of the engine compartment to get to this one little rubber gasket which was a multi day job.

You need your SSN ASAP, as you won't be able to get a drivers license without it. (Some states issue a restricted DL to illegals who don't have an SSN, and all state will issue DLS to people who have a visa but aren't eligible for an SSN, such as a trailing spouse on an H-4.)

In most states you can buy and register a vehicle without having a license, though it will be easier with a local license.

According to "Consumer Reports" they note that use of winter tires is more important than AWD. AWD does not improve handling or stopping, just getting moving from a dead stop.

There is a price premim for AWD and then there is a hit from increased fuel consumption.

BTW, if you go the used car route, look for the more upscale models. We purchased a 2013 Toyota RAV4 a year back via the Toyota Certification program. Our car is the "limited" rather than the SE or LE. For not much more we got power seat (important for two drivers) and lane change monitor.

Also consider Mazda CX-5 or CX-9. Younger daughter bought a certified 2015 CX-5 last fall.

The lane change monitor compensates for the blind spots.

Fully endorse the winter tyres vs AWD. A rear wheel drive car with snow (winter) tires (tyres) will be better in most snow conditions than AWD. Ideally you would use 4wd with snow rubber. However, when it comes to ice, you really need studs or chains.

OP does not State where in Idaho where she will be living. Given the low population, the car shopping should be over a broader area. For example, the Toyota dealer in Salt Lake has a larger selection than the dealer in Pocatello.

In poor traction conditions I'd take front wheel drive over rear wheel drive, unless it was a VW Beetle (original design, not the Golf coupé).