I got into the show in the late '80s, just in time to watch the premiere of season 26 on my local PBS affiliate in the US. But other than getting into the franchise just as the show was ending for a decade and a half, I was extremely lucky, really. I had two PBS stations in broadcast range who carried the show at the time and showed omnibus movie-packaged stories every weekend on Saturday and Sunday nights, respectively.

One of said stations pivoted directly from the season 26 showings over two weeks (unusually done as two serials each week) to starting over from An Unearthly Child and working through the whole show (minus the missing/incomplete stories) in order. They showed most of the first two seasons (through The Chase) as an all-night marathon on Saturday night. I was 10 at the time, and that was the first all-nighter I ever pulled.