Dragon Ball Super: Super Hero

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This level of debate is what I sought to avoid - getting into the murky waters of how Japanese anime is handled rather than continuing to be straight-line serialized or anthology content.

From the more helpful posts, what I'm getting out of it is, as a starter, Dragon Ball began with "Dragon Ball". And then it became Dragon Ball Z.

The short of it is, you start with Dragon Ball and if you don't want to watch chibi-characters at the height of their weirdness, just go to Dragon Ball Z which is the first incarnation of the anime as we tend to see it in pop culture today.

Best places to do this are probably Crunchyroll or Funimation unless they can be easily DL'd somewhere because the on-disc releases have been a mess to invest into.