I'd recommend two episodes that aren't very 'canon':
Jose Chung's From Outer Space. This is one of my all-time favorite X-files episodes and actually serves as a good introduction to the main characters because it portrays them so broadly.
This is the questionably accurate backstory of a supporting character and doesn't really include the main characters except as bookends. However, it perfectly captures the general tone of the series.
In terms of 'watching every episode', X-files was shot before the current trend of overarching plots. Until Gillian Anderson (the actress, not the character Dana Scully) got pregnant (season 2), it was a pure monster-of-the-week series.
From that point on, the X-files alternated 'mythology' episodes with 'monster-of-the-week' episodes. So there are a lot of episodes you can miss without missing the overall story. The 'overall story' is also less cohesive than a Breaking Bad or Game of Thrones - it tends to be presented as a series of mysteries that never get solved, so don't expect a tight resolution pulling from every little crazy event they experience.
Some of the best episodes are difficult to jump straight into because they require greater knowledge of Scully and Mulder's character development, but my personal favorite standalone episodes are the comedic ones like "Bad Blood" and "Humbug", and other memorable ones like "Post-Modern Prometheus" and "Milagro".
I hope you love the show! Despite having seen many others after it, The X Files remains my single favorite TV show.
I'd highly recommend listening to The X-Files Files podcast along with your re-watch. Its hosted by comedian/actor Kumail Nanjiani, who is a long-time X-Files fan.
He has celebrity guests, as well as people who worked on the X-Files, come on the podcast and they talk about 2 episodes of the show each. He's on Season 5 now, but all of the old episodes are available.
Its a great way to hear some discussion about the episodes if you're re-watching on your own, as its difficult to discuss with people who haven't watched the episode you just did in 20 years. Plus he gives you a bit of a heads up on some of the less-good episodes, so you can either skip them outright or go in with lower expectations.
If you just want to see all the crazy monster of the week episodes, start with Home off of season 4. The great Mutato off season 5. But if you want to actually follow the story line start from episode 1. They usually make the seasons with about 6 episodes about the story arch and the rest of the episodes of monsters if the week, which have nothing to do with the main story line.
The first season is kinda slow but the first 2 episodes set up the whole series. In the middle of the seasons they have the monster of the week episodes, and some of them are better than some story arch episodes. But if you get into it don't watch the first movie until you finished the 5th season, watch it before you start the 6th season.
The rest of the series makes more sense.