The best way to watch serials is definitely one at a time, or a few at most.
Chapters really don't have self contained plots. Even the overall structure of complete serials is more of a theme than a plot. While one event leads to the other, each has little barring on previous ones once the cliffhanger is resolved.
Serials were very similar to early television shows and older comics. There was no real continuity, once a chapter or episode is done things are reset and repeated in a slightly different way. The constant elements being the heroes fighting the same villain for weeks until it ends.