I liked the first Budokai game. Never did play the second though. The first was generally a good summary/condensation of the storyline.

Personally I would recommend getting into Dragonball more through the manga, which is available in English and should be carried by any bookstore--sometimes its located in the Teen isle rather than in the manga section (start with the first volume of DB, rather than the first volume of DBZ).

Even in its original Japanese, DBZ has a sort of dragged-out quality to it (the whole "one fight can take twenty episodes" thing), which I personally like, but its one of the chief reasons most people don't care much for it. The original DB, too, has a similar issue though not taken to the same extremes. The manga, however, generally lacks this. And reading a comic is easily far quicker than watching a show.

When it comes to the dub, honestly I think the worst thing about it is the music. A few censorship cuts won't kill a show, but music will make or break good entertainment (just imagine if the entire soundtrack of Star Wars consisted of music from Barney the Dinosaur). There's nothing wrong with the US music for DBZ, it just doesn't stand out, and it gets monotonous. the Japanese music doesn't, and I garuntee nobody who hears Cha-La-Head-Cha-La, Bokutachi Wa Tenshi Datta ("We Were Angels") or DBGT's Dan Dan Kokoro Hikareteku will ever forget them.

(The music, in fact, is one of the main things I like about anime).

EDIT: By the way, I'm not totally convinced that all the points that video brings up are edits. Goku's father being a scientist for example... remember that when they made that episode, the Bardock special hadn't been made yet, and probably Toriyama didn't even have an inkling of an idea that he'd eventually do a story about Goku's dad. So they could say whatever they wanted about him and it would stick.