Now that was just one game and it covered +80% of the franchise, there are a few arcs missing from Dragonball, but you should be able to understand the full story anyway.
If you want to see more of DBS, you can play Xenoverse, you have to play the Parallel Quests, of course. I don't think you'll be able to fully understand DBS like what Kakarot does for Z, though. It goes for GT, as well.
About the first arcs of Dragonball, there must be some old game, probably not that entertaining due to being from the early 90s, late 80s. Although, I think there was a Piccolo Daimaoh game released in the mid 2000s.
If you want GT, Final Bout is the only one IIRC. It has SS4 Goku, Kid Goku, GT adult Goku, GT Trunks, GT Pan, and Ohzaru Vegeta Baby. Can't remember how the story mode goes.
The 2000s had games that had more of GT now that I think about it, with many characters, but again I cant' speak of its story mode.
The only missing parts are goku's first meeting with kami as well as End of Z.
The GBA titles are also a solid option. Advanced Adventure goes from Pilaf to King Piccolo, and the LoG trilogy covers all of Z (although the 1st game cuts corners, it covers most of the major events). GT Transformation also goes as far as Baby.
This just leaves the 23rd Tournament and the last half of GT not covered by GBA games.
If you just want a fast but accurate way to play Raditz-Cell then Budokai 1 is a solid choice. It obviously skims over a lot and doesn't cover pre-Z or Buu, but it gives you the gist of the Raditz-Cell story and has really good cutscenes.
Tenkaichi 2 actually isn't a terrible option either. It covers almost every major fight from Raditz to Omega Shenron, and offers text to explain what's going on. And if has some okayish cutscenes for certain moments. And it includes most of the Z movies, but doesn't really attempt to make them fit (which is understandable).