In Dragon Ball Z: Buu's Fury it is shown that the Janemba event happens just after Goku arrives back in Other World, at the same time that Mr. Satan is befriending Innocent Buu. In Dragon Ball Z: Shin Budokai, the story occurrs during a time of apparent peace shortly after the battles with Majin Buu. Since episode 241 (which is set approximately one day after the tournament), the Dragon Team still on Earth believe Gohan to be dead in the series, while in the movie they interact with him as if this is not the case. The movie occurs 9 days after the tournament, as shown on Videl's watch. Dende explicitly stated in episode 240 that the Z Fighters would have to wait four months to use the Dragon Balls again due to Bulma and the others summoning Shenron and wishing for Vegeta's rampage to be undone. Yet, if this movie takes place a few days later, the Z Fighters on Earth should not have been able to summon Shenron. When Goku and Pikkon are being introduced in the tournament at the beginning of the movie, Goku is referred to as the defending champion, even though in the last Other World Tournament it was a draw due to them both touching the ceiling during the battle. However, during their original battle, Goku was briefly declared the winner of the first tournament before Grand Kai told them touching the ceiling disqualified them.
You're in luck - there are multiple places you can watch Dragon Ball. The series is available on streaming services such as Funimation, Crunchyroll, and Hulu. If you'd like to own it, you can buy the episodes or the home video releases on Amazon. 781b155fdc