The "series" people are referring to are the television shows, with part 1 starting in 1971 and the most recent, part 5, airing just last year. A Woman Called Fujiko Mine is also a tv series, but it's mostly about Fujiko, with the other characters sometimes appearing here and there.
There are also feature films and television specials, the latter of which are like longer episodes with bigger budgets. You can watch these in any order you want as they're standalones, even the crossover with Detective Conan.
You can read the manga if you want but you absolutely don't need to. The manga is its own thing, and the anime is not a straight adaptation of the manga at all.