After consulting the Lurker’s episode guide (http://www.midwinter.com/lurk/eplist.html), I give you my quick reviews of the first season episodes. Please keep in mind that this is purely my subjective opinion, and YM, of course, MV:
Midnight on the Firing Line - necessary for understanding the roots of the Londo/G’Kar hostility.
Soul Hunter - The Soul Hunters do appear later on, including in a post-show movie, but they aren’t generally important enough to the story arc to watch this if you don’t care to.
Born to the Purple - Adira will show up again, and it’s kind of fun (Sinclair trying to pretend to be a tough guy is a hoot in its unbelievability).
Infection - skippable.
The Parliament of Dreams - Some clues about what happened to Sinclair during the war, but you also have to put up the intro of his girlfriend and their relationship. I like this show primarily for G’Kar’s “fishies” song and the business-like assassin: (Reading off a list: “You will know pain”–zzapp!).
Mind War - The only reason I can see for watching this is the introduction of Bester and the PsiCorps, and G’Kar’s speech about the ant at the very end. The guy who plays Jason Ironheart is painfully bad, and the thing he turns into at the end would embarrass a really bad Star Trek episode.
The War Prayer - Not necessary, but I like the Londo subplot.
And The Sky Full Of Stars - More on what happened to Sinclair during the war.
Deathwalker - Not necessary, but not a bad episode.
Believers - A lot of people really like this one, but I usually skip it.
Survivors - skippable.
By Any Means Necessary - skippable unless you enjoy Londo and G’Kar quarreling.
Signs and Portents - The first really good and important episode of the season. Do not miss it.
TKO - Ick. Stay away.
Grail - Not necessary, but it’s got David Warner in it.
Eyes - The PsiCorps returns and there’s a kind of review of the series up to this point; important mostly for the reasons why Ivanova hates the PsiCorps.
Legacies - Not necessary unless you like the Talia/Ivanova relationship.
A Voice in the Wilderness - Absolutely necessary. Do not miss.
Babylon Squared - Absolutely necessary. Do not miss.
The Quality of Mercy - The machine featured here will turn up again twice, and Londo’s attempted corruption of Lennier is entertaining (and includes a LOTR reference).
Chrysalis - Absolutely necessary. Do not miss.