Some people bounce off Season 1, hard. There's a lot of dire episodes near the start. In the first eight, Infection, Mind War and The War Prayer are pretty terrible; Midnight on the Firing Line and Born to the Purple have some good elements but are let down by some awful acting; And the Sky Full of Stars is great but if you dislike Michael O'Hare's very reserved acting style you're going to have trouble with it; Soul Hunter has a great idea but a rather cheesy resolution; and only The Parliament of Dreams is decent (mainly due to the excellent relationship between G'Kar and Na'Toth - "You will know fear, you will know pain and then you will die, good day!", though even that has the painful Sinclair romance subplot.

My recommendation would be to check out Signs and Portents. It's only a few episodes down the line (episode 13 of S1), is one of the best episodes of the first season and is the first episode that really delves into the ongoing story arc in any detail, whilst still being approachable to newcomers. There's also And Now For a Word, which is much later (Season 2, episode 15) but is framed as a news report from the station which provides a late-entry point for new viewers. It will spoil stuff from earlier, but I think it's a good representative of the series just as it's hitting its stride.

BABYLON 5 isn't for everyone. The acting style is very theatrical and dialogue-focused, which can be unusual for people used to the more realistic and action-focused style of recent SF shows like LOST and BSG. It also had a tiny budget (it's not a big-budget show by any stretch of the imagination), about one-third of what STAR TREK: THE NEXT GENERATION and DEEP SPACE NINE had per episode. On that amount of money, the CG effects, the number of extras they had to bring the station to life and some of the bigger sets are actually pretty impressive.

On the downside, some of the actors are bad (Michael O'Hare, who plays Commander Sinclair, is pretty wooden; fortunately he doesn't stick around for that long) and the show's attempts at comedy and romance are usually embarrasing. On the upside, some of the other actors are brilliant: Andreas Katsulas as G'Kar and Peter Jurasik as Londo develop into the best double-act in SF history; Jerry Doyle as Garibaldi starts off very limited but develops into a strong actor quite well over the four seasons; and Stephen Furst as Vir and Bill Mumy as Lennier make the most of their limited roles, particularly in Season 2 and later (Furst can be quite annoying at, erm, first).