Babylon 5 is perhaps the only television show ever to have a multi-year plot structured in advance of its creation, and the follow-through for that is entirely effective. However, the plotting is so far-sighting, that it can be initially imposing - particularly given that the pilot movie and first season of the show are occasionally less-than-competent.
I was a fan when it aired, and, with some trepidation, I decided to rewatch it again recently. Happily, the show was still good, and easily held its own against other 90's SF, like Buffy or The X-Files. The Renaissance Poet watched it as well for the first time, and since she didn't have a nostalgia cushion, so I decided to blast through the crap and get to the good stuff. By and large, it worked.
There's another minor complication - particularly in the first and second seasons, episodes aired out of order. I don't know if this was fixed for DVD releases. I do know that seasons 1 and 2 on Hulu are in airing order, not proper order. Generally this isn't terrible (it wasn't gutted like Firefly) but occasionally watching in the proper order makes the show make much more sense, especially in season 2. A master chronological list is available here. Bookmark it!
Season 1 is the most iffy of all the Babylon 5 seasons. First of all, as a television show, B5 was struggling to find its footing, especially given that no science fiction show other than Star Trek had ever aired successfully on American TV. Second, the plot of B5 unfolds slowly, and it's hard to see it as anything other than a procedural/monster-of-the-week show most of the time.
It's easiest to sort the episodes into three categories - those critical for the main story (which are also generally the best episodes), watchable episodes which bring up somewhat important character or universe background, and those which are just plain bad.
The best way to go about watching the season is to watch the first two episodes, in my view. If you think "Hey, this is fantastic!" then watch 'em all. If you think it's moderately interesting, then watch the first two categories. If your patience is tested...well, sorry about that, but it does get good. I swear. Watch the critical episodes and get to Season 2 as quickly as you can.
1-01 - "Midnight on the Firing Line"
1-02 - "Soul Hunter"
1-05 - "Parliament of Dreams" *
1-06 - "Mind War"
1-08 - "And The Sky Full of Stars"
1-13 - "Signs and Portents"
1-16/17 - "A Voice in the Wilderness" pt. 1/2 **
1-18 - "Babylon Squared"
1-21 - "Legacies" *
1-22 - "Chrysalis"
* In terms of plot, these aren't absolutely necessary. However, they both introduce important characters, and are better-quality than others.
** If you're really, really disliking the show after the first couple of episodes, skip to this one. It's early B5 at its best - good character development, interesting storyline, and for the first time, it has a successful sense of humor! If this doesn't grab you, it may be that nothing will.
1-03 "Born to the Purple" *
1-12 "By Any Means Necessary"
1-19 "The Quality of Mercy" *
* These episodes are directly referenced later on, more than once in certain cases, so they're somewhat important. On the other hand, they're not terribly good, particularly "Born to the Purple." A plot summary may be the best way to go.
1-04 "Infection" (this is pretty clearly the single worst episode of the entire five seasons)
1-07 "The War Prayer"
Most of the second season is a step above the first in quality and importance. One episode, though, just kind of raises a stink: 2-04 "A Distant Star"
Babylon 5 had one pilot movie, and five other made-for-TV movies.
"The Gathering" - This is the pilot movie, and has several problems. First of all, it's kind of bad. Second, it was scored by a totally different composer than the rest of the series, and B5's music is one of its most distinctive and good qualities. It was later re-edited for TNT with proper music and some of the crap eliminated, but it's still not terribly good. I advise skipping it, or watching the edited version after you're sure you like the series.
"In the Beginning" - A prequel movie made for TNT. It's a little contrived, but has some occasional moments of excellence. I would recommend watching it, at one of three points: as the entry into B5; after the two-parter in season 3; or when it was produced, between seasons 4 and 5.
"Thirdspace" - Made at the same time as "In the Beginning," it's kind of a reimagining of Babylon 5 as a big dumb action movie, and reasonably successful at that. Watch after its chronology at any time (around the middle of Season 4).
"River of Souls" - Set after the end of the last normal episode, but before the grand finale. It's pretty good. Watch anytime in the second half of the fifth season.
"A Call to Arms" and "Legend of the Rangers" - Two pseudo-pilots for spinoffs, one of which came to be, the second of which didn't. I didn't like "A Call to Arms" and I heard "Legend of the Rangers" was worse. I'd skip 'em.
In conclusion, I am a geek.