You have a couple of options.
1) If you want to know about how the series started, Dragon Ball (the first one) is a great place to start. However, it hasn't been redubbed so you would have to watch it with Funi's '90s English dub or the original Japanese dub with subs.
2) If you're only interested in DBZ because this game seems to be focusing solely on DBZ and Super, I'd highly recommend Dragon Ball Z Kai. There's Blu-Rays for each saga now (I believe) in English dub with the original Japanese score. This is the redub and no filler, more true to the manga version of the anime. A lot less episodes overall than the original run of DBZ.
From there, you have the option of watching the Battle of Gods and Resurrection of F movies (these two are actually the only two canon movies) and the Bardock and Future Trunks Specials. These are all also on blu-ray.
However, they are arguably not that necessary to watch unless you really end up liking the main series (DBZ) and want to have some more of it.
After all of that, you could then start watching DB Super after like Episode 28 -- Japanese subs. This you could access on Crunchyroll.
But mainly, DBZ Kai is what you'll want to watch if anything. Highly recommend it.