I think the most important X-book of the 80s would be Uncanny X-Men with arcs like the Dark Phoenix Saga, Days of Future Past, and crossovers like Secret Wars, Inferno, Mutant Massacre and Fall of the Mutants in the late 80s. Byrne worked worked on Dark Phoenix and Days of Future Past.
The 80s also had Classic X-Men reprinting older stories with some pages from Uncanny added for continuity. This could be interesting if you want to read all the older stuff.
I personally love X-Factor that started in the 80s and highly recommend it. And if you're a Wolverine fan, his first limited series was in the early 80s and it was relaunched at the end of the 80s. I also remember reading a limited Nightcrawler series from the mid-80s. I thought it was fun but might not be interesting unless you're a fan of the character.
If you want more stuff from John Bryne, I think he worked on Alpha Flight during the 80s. I've never checked it out so I don't know if it's good or not.
This page has a really good summary of all the important events, Claremont's work on the X-books during the 80s, and info about when new characters appeared:
http://www.faqs.org/faqs/comics/xboo...section-4.html
I think the costume has to do with how much of a part the costume has in making the character recognizable. Facial features change a lot from one artist to another so they can't always expect readers to recognize characters based on this. The more unique a character design is, the easier it is to create a new costume for them.
Some characters can go through costumes and even wear normal clothes and still be recognizable because of really unique character design. I'm thinking about Mystique's skin, Wolverine's hair, and claws Bishop's tattoo or even Cyclops' visor. On the other hand, characters like Jubilee, Magneto, Kitty Pryde, etc don't have any characteristics that 'jump out' at the reader other than their costume. I'm not saying they shouldn't update the costumes, I'm saying it's a lot trickier to change a costume when it's the main element of the character design.