My girls loved going in the car and settled down straight away. Even asleep before we got 2 minutes down the road! For the first trip home, that sounds good, just make sure you have puppy pads, blanket and wet wipes handy
. After the first journey we put them in the place where we wanted them to travel the majority of the time i.e. in a crate in the back. However, our youngest was travel sick so we had to adapt to that - even buying cars with stiff suspension for her - I know.
In the last few years, we finally had a car where we could fit 2 crates side by side. We had soft crates that folded down easily. We also used them in the apartment and hotel rooms as they were easy to move around etc. We used the crates on journeys where it wasn't too long or we didn't have loads of luggage. For holidays and longer car trips, the girls went on the back seats, on their beds, wearing a good harness that clipped into the seat belt.
On long journeys they much preferred this as they could stretch out more and also benefit more from the air con. It was also easier for me to keep an eye on them as one wasn't the best traveller (travel sick). So we changed the transport mode depending on journey, time, temperature etc.
The most important things to think about (which I'm sure you know), is that in an accident you don't want the dog to become a missile - hence the harness,crate etc and you don't want them to be able to escape into traffic if a door or the boot is opened in an accident or by someone else.