My first Barks-story, as far as I can remember, was
The runaway train (WDC 195). It's the tenpager in which Donald and his nephews are staying home, while outside a storm occurs. Donald is watching a gangster movie on tv, and Huey, Duey and Louie are busy with a Junior Woodchuck project involving miniature trains. Then suddenly the movie is interrupted for a special newsflash and message to a certain professor. It appears two trains are about to crash onto each other and they can't be reached to warn them. So they ask the professor to come up with an answer. However, the professor doesn't, and it's up to H,D&L to provide a solution by using their miniature trains, and a bit of help from Uncle Scrooge.
It was not just my first Barks-story, but also one of the very first Duck-stories I've ever read. Even as a kid, I felt this story was better than the others. At first the story might seem a bit dull, with the Ducks doing nothing but staying inside and just talk, and talk and talk, but there is a really great sense of suspense, even though the Ducks are not personally involved in the train-disaster that is about to take place. Also, the reactions of H,D&L and Donald are perfectly contrasted and timed.