Yes, do start with Dragon Ball. Z may be the more popular in terms of anime but it is the culmination of everything that happened in Dragon Ball that helps bring Z to life. 156 episodes but the entire world is full of life and flair.
After that, it gets a bit tricky. If you're watching the series dubbed, best to go with Kai. The dub for Z is pretty horrendous. If subbed, well you're not exactly missing too much by seeing Kai but the performances of the VA aren't in their prime unlike Z. What I might recommend you do is watch Kai subbed and then if you feel you enjoyed it, set some time aside to be able to go through Z subbed. Some scenes are better in Z, some in Kai.
Basically, you'll get a better understanding in a way of everything. Kinda. Maybe.
After Z/Kai, there's a little OVA special called "Yo! Son Goku and His Friends Return!". It's nothing very special but if you happen to like the little downtime moments in the series, this one's pretty good. Will also give some context later on for mentions of "Vegeta's brother".
After that, the two movies "Battle of Gods" and "Resurrection F". Ignore the Dragon Ball Super versions of these twp as they were butchered pretty hard.
Next up is Dragon Ball Super. Start with Episode 18 and don't look back until the series end at Episode 131. After that is the DBS Broly movie and.... You're pretty much done.
Oh, there are some old DB and Z movies but you can watch those on your own time as none of them are canon. What are canon though are the two TV specials "Bardock: The Father of Goku (Watch this basically when Goku begins to fight Frieza) and "The History of Trunks" (Watch pretty much after Trunks divulges his backstory to Goku)