For the dog to not stain or scratch the seat with its claws, you can buy a cover for the seats, which will not cost a lot either.
Wraps or covers come in many forms and are designed for both front and rear seats. There are also covers for door panels. They are also not very expensive, but they protect plastic, leather and wooden linings well from animal claws.
Small dogs can also be carried in carrying bags or carriers. There are many options, from rag to plastic folding. The price depends on the material and type. The main thing is that they are attached to the seats with seat belts, or even through the Isofix fastener, which ensures the animal and you proper safety on the road. It is clear that a large animal cannot be put in such a carrier, but if you are sure that your buddy subsequently does not grow into a polar bear, buy such a device. After all, it is possible to carry a pet in it not only in your car, but also in public transport.
By the way, it would be nice to partially isolate large animals traveling on the second row, so that the dog, in a fit of feelings, does not climb, licking you behind the ear and thereby does not distract you from controlling the driveway. To do this, you can install a mesh screen between the backs of the front seats. It costs about 10$, allows the dog to be near you and at the same time not interfere with your control of the road. And since the screen is mesh, it does not overlap the view and allows you to control what is happening behind through the driving mirror. If you prefer not to be distracted from the road when turning back to see what your dog is doing there, you can buy an additional panoramic mirror and attach it to the windshield using a sucker so that you can see what is happening on the second row. It costs 5-10$ if not less.
Often, dogs lack air in the cabin, especially if the car does not have air conditioning. In order to prevent this situation, drivers are forced to open the windows where the dogs stick their faces out. And this is not always safe. An annoyed dog may try to jump out of the window when you open it, and although it is fastened, it still has a certain degree of freedom.
In order to let the dog breathe freely and at the same time not try to lean out the window, there are special grids / gratings. Foldable, made of plastic, it is inserted between the lowered glass and the upper edge of the door, providing both an influx of fresh air and an obstacle. By the way, these devices are very useful if you often leave the dog in the car in the parking lot. Your fluffy friend will definitely not be stuffy, especially if you ensure the flow of air not from just one, but from two sides. A set of a pair of gratings will cost about 20$.
So, having decided to go on a road trip by car or just to a grocery store with your dog, think about whether you have done everything to make it safe. After all, dogs are our friends, and friends must be taken care of.