Urusei Yatsura is a monster that few new viewers could ever hope to catch up with. There are 34 volumes of the manga, 195 TV episodes, 12 OAVs, and 6 movies.
However I haven't attempted to catch up with all of it, and I wouldn't recommend making the attempt.
In any long series individual instalments will vary in quality. In my experience the quality of Urusei Yatsura is not a continuum. There are good to excellent instalments, and there are instalments that should never, ever, see the light of day again, with very little inbetween.
Fortunately Beautiful Dreamer (1984) directed by Oshii Mamoru is one of the former.
I'm not going to give a detailed synopsis for Beautiful Dreamer.
Apart from anything else I'm not sure it is possible to write one that makes sense.
The set up is a Groundhog Day (1993) scenario centred on preparations for a high school festival, crossed with Urashima Taro (which is kind of a Japanese equivalent to Rip Van Winkle).
The key to the set up is that Lum has been enjoying that mythical high school life with her friends and (hopefully) boyfriend Ataru and wants the feeling to last forever.
Be careful what you wish for.
The difference is that it affects the entire cast and those that notice begin to disappear following the crazy logic of the dreamworld. After all they can't be permitted to disrupt Lum's happy dream.
To avoid making a villain out of the heroine a sort of villain, the dream maker Mujaki, is introduced and "defeating" him forms the resolution of the film.
Beautiful Dreamer never really makes that much sense but the atmosphere and style more than make up for that lack.
To be honest not that much really changes in Beautiful Dreamer. Granted it is clear that Ataru loves Lum (after a fashion), he couldn't have woken up otherwise. However the shows basic dynamic of Lum chasing Ataru whilst Ataru chases every other girl in sight and then Lum shocking Ataru with who knows how many thousand volts doesn't really change.
But hey it's Rumiko Takahashi so a final resolution to the romantic storyline is never really expected anyway. :)
Having said that Beautiful Dreamer is a fun, if more than somewhat surreal, film to watch, and one that I think stands alone quite well. If you wanted one exposure to Urusei Yatsura you could do a lot worse, and would struggle to do better.
Day 1 - New Kimagure Orange Road: Summer's Beginning (1996)
Day 2 - Naruto Shippuden The Movie (2002)
Day 3 - Galaxy Express 999 (1979)
Day 4 - Steamboy (2004)
Day 5 - Urusei Yatsura 2: Beautiful Dreamer (1984)
Day 6 - ???
Day 7 - ???
Day 8 - ???
Day 9 - ???
Day 10 - ???
Day 11 - ???
Day 12 - ???
Day 13 - ???
Day 14 - ???
Day 15 - ???
Day 16 - ???
Day 17 - ???
Day 18 - ???
Day 19 - ???
Day 20 - ???