Dragonball the original with Goku as a child has a lot more slapstick PG comedy elements with fighting mixed in. It's more of an adventure show where Goku wants or needs to find the Dragonballs for some wish or another. In between, they go to the fighting tournaments which is probably the low point in the series - which ironically Dragonball Z fighting are it's high points - merely because they feel stretched out. If you want the full lore, you could start here.1. Should I watch the Dragonball series?
2. If yes, where should I start. The very beginning or elsewhere?
If you start with Dragonball Z, I'd actually recommend Dragonball Kai instead. It has some minor graphical updates and removes A LOT of filler nonsense that serves no purpose. There's plenty of reason for everyone to fight and train and get stronger here with the backlore of the Dragonballs used to revive dead heroes or undo serious damage to the planet and it's population. Rose tinted glasses and nostalgia alike, I find the series to be one of those defining childhood experiences. Watching the Super Saiyan transformation for the first time with the extensive build-up is inspiring. It's, I think, an anime first to have a character like Goku whose gentle and kind but also serious and capable in ways that's pretty much copied into other animes since-forth. You may find him to be a little too trope-y in that regard but he's the original nice-guy in anime. (As far as I know.)
I'd recommend this one.
Then there's also Dragonball Super which continues after Dragonball Z so start only after you finish with Z.
Dragonball GT is pretty lame. It's almost like they tried to return to their roots with the original Dragonball except none of the comedy. The fighting seems to be a checklist which all seem to start and end the same way. If you watch it, you'll be grateful that it ends so quickly.
Depends on what you like. Animation is at least fair. Story line is good enough. I don't like recommending things because personal taste can be severely altering to a good or bad experience.3. If no, any strong reasons as to why? Any other recommendations to sate my want?
But you've probably already seen Death Note. If you haven't, I'd recommend the first season.
Berserk only has one season (thought I hear there's a second one finally coming out later this year?) which has high animation quality, blood, and the story is pretty damn awesome too until the confusing last episode or two.
Hajime No Ippo is one I've been watching. An anime with realistic approach to Boxing. No super powers. The 'Chosen one' is a side character with an obnoxious personality so you see the average-man, Ippo, struggle as a young Boxer. Fights are interesting and serious, opponents are interesting and inbetween fights, there's great comedy elements in the training phase episodes. Currently 3 or 4 seasons?