Drive to Survive was my gateway drug as well. Since then, I've watched every race, and qualifying if I can help it (which can sometimes be even more exciting). I'd suggest watching current races - you'll know most of the people involved from watching DtS, which makes it much more compelling.
Also, I've found a few podcasts that I listen to during the week that help me stay up to date with the storylines of the season. In particular, Missed Apex[1] and Shift+F1[2] are my go-tos. The former is a little bit snarkier and opinion-based, the latter is more straightforward and factual - both are good. Check out their race previews/reviews, it will give you some things to pay attention to when watching a current race.
Also, I've found a few podcasts that I listen to during the week that help me stay up to date with the storylines of the season. In particular, Missed Apex[1] and Shift+F1[2] are my go-tos. The former is a little bit snarkier and opinion-based, the latter is more straightforward and factual - both are good. Check out their race previews/reviews, it will give you some things to pay attention to when watching a current race.
[1]: https://missedapexpodcast.com/
[2]: https://www.f1.cool/