The Weasley family is known for their hospitality and kindness that spreads to each of the children. Although they don't have much money, they always make do with what they have. That said, their means of transportation or the items they purchase often place them under scrutiny from more noble families, like the Malfoys. Nevertheless, this doesn't stop them from ensuring their children are granted every opportunity possible to succeed while studying magic. Thanks to a new theory, this can even be traced as early as when Ron and Hermione meet for the first time.
In Harry Potter's first year, he and Ron share a space on the Hogwarts Express and form a fast friendship. The two are later joined by Hermione, who quickly makes a note of the dirt on Ron's nose. Thematically, the scene helps show how Hermione is prone to noticing tiny details while Ron is much more carefree with how he lives his life. However, according to Reddit theorist RedditingAtWork, there's an even more clever connection to his home life and their means of transportation.
In Harry Potter in the Chamber of Secrets, Ron, Fred and George all use their family's flying car to steal Harry away from the Dursleys. It later takes Harry and Ron to Hogwarts, where the Hogwarts Express nearly hits them. Almost immediately, the convenience of having the vehicle is evident.
However, if it's so helpful, why wasn't it seen in the first film, and how did the Weasley's get to King's Cross station without it? Aside from vehicular transportation, there's also the ability to travel by Floo powder. This powder allows the user to go under a chimney, say their destination, like Diagon Alley, and quickly travel to the destination.
Although the franchise never explicitly states that there is a chimney at King's Cross, it's possible that the Weasley's found a nearby one to get to the station. It's then shown that Mrs. Weasley is trying to clean Ron's nose of dirt, but because he's running behind, he doesn't care if he's a little dirty. That said, this moment shows that while the Weasleys aren't the most wealthy, they make up for it in being resourceful.
The Weasley family knows that they can't always provide the best for their family, but that doesn't mean they can't have them participate with the other, more fortunate children in their class. This is shown by how adamant Molly is with cleaning Ron's nose, so he doesn't look like a mess for his first year. Of course, they also may have already had a car to travel with, but if they were in a rush, it would explain why it didn't appear until the second film.
Ron's family learned quickly that it's not about what they can have but rather what they can do with what they've provided. A great example of this is the possibility that they still know how to travel efficiently if they don't have a car, even if it isn't the cleanest. Even though they may not have as much as the Malfoys, the Weasleys never stop ensuring that their children understand that if they don't have the best, they can still be the best, even if it entails stealing the family car to get to school on time.