I know what you're saying Jan, and I'm definately a completist at heart who'd love to watch the whole thing. I'm just being visited by a friend who's only going to be in the country for a week. Rather than watch the first 2 series and miss the last 3, I'd like to try and get as much as possible watched through-out, since I don't know when I'll get another chance to watch it.
Watch them from the beginning, in this order, and get as far as you can before your friend leaves. Then rent[1] the rest, and finish.
The Gathering (pilot) [2257]
Season One ("Signs and Portents") [2258]
Midnight on the Firing Line
Soul Hunter
Born to the Purple
Infection
The Parliament of Dreams
Mind War
The War Prayer
And The Sky Full Of Stars
Deathwalker
Believers
Survivors
By Any Means Necessary
Signs and Portents
Grail
Eyes
A Voice in the Wilderness - Part 1
A Voice in the Wilderness - Part 2
Babylon Squared
The Quality of Mercy
TKO (why not right after Signs and Portents ?)
Legacies
Chrysalis
Season Two ("The Coming Of Shadows") [2259]
Points of Departure
Revelations
The Geometry of Shadows
A Distant Star
The Long Dark
A Spider in the Web
A Race Through Dark Places
Soul Mates
The Coming of Shadows
GROPOS
All Alone in the Night
Acts of Sacrifice
Hunter, Prey
There All the Honor Lies
And Now For a Word
Knives
In the Shadow of Z'ha'dum
Confessions and Lamentations
Divided Loyalties
The Long, Twilight Struggle
Comes the Inquisitor
The Fall of Night
Season Three ("Point of No Return") [2260]
Matters of Honor
Convictions
A Day in the Strife
Passing Through Gethsemane
Voices of Authority
(this was originally meant to air before "Passing Through Gethsemane," but since the events of this episode tie into the beginning of "Dust to Dust," and aren't mentioned at all in "Gethsemane," the initial airing order is actually an improvement)
Dust to Dust
Exogenesis
Messages from Earth
Point of No Return
Severed Dreams
Ceremonies of Light and Dark
A Late Delivery From Avalon
Sic Transit Vir
Ship of Tears
Interludes and Examinations
Walkabout
War Without End, Part One
War Without End, Part Two
Grey 17 Is Missing
And the Rock Cried Out, No Hiding Place
Shadow Dancing
Z'ha'dum
Season Four ("No Surrender, No Retreat") [2261]
The Hour of the Wolf
Whatever Happened to Mr. Garibaldi?
The Summoning
Falling Toward Apotheosis
The Long Night
Into the Fire
Epiphanies
The Illusion of Truth
Thirdspace (TV Movie) [obviously in 2261]
Atonement
Racing Mars
Lines of Communication
Conflicts of Interest
Rumors, Bargains and Lies
Moments of Transition
No Surrender, No Retreat
The Exercise of Vital Powers
The Face of the Enemy
Intersections in Real Time
Between the Darkness and the Light
Endgame
Rising Star
The Deconstruction of Falling Stars
Season Five - ("Wheel of Fire") [2262]
No Compromises
The Very Long Night of Londo Mollari
The Paragon of Animals
A View from the Gallery
Learning Curve
Strange Relations
Secrets of the Soul
In the Kingdom of the Blind
A Tragedy of Telepaths
Phoenix Rising
The Ragged Edge
Day of the Dead
The Corps is Mother, The Corps is Father
Meditations on the Abyss
Darkness Ascending
And All My Dreams, Torn Asunder
Movements of Fire and Shadow
The Fall of Centauri Prime
Wheel of Fire
Objects in Motion
Objects at Rest
River of Souls (TV Movie) [2263]
The Legend of the Rangers [pilot movie and series late 2265 to late 2269; "just under 3 years after the events of 'Objects at Rest.'" This means it will be set in late 2265]
A Call to Arms (TV Movie) [January 2267]
Crusade [January 2267 - December 2271 was planned]
This ordering, which JMS specified, ignores the uniform change in favor of maintaining continuity of storyline, except that I moved War Zone to position 1.
War Zone (chronologically takes place immediately after A Call to Arms.)
Racing the Night
The Needs of Earth
The Memory of War
The Long Road
Visitors from Down the Street
The Well of Forever
Each Night I Dream of Home
Patterns of the Soul
The Path of Sorrows
Ruling from the Tomb
The Rules of the Game
Appearances and Other Deceits
Babylon 5 - The Lost Tales - Voices in the Dark (Direct-to-DVD, #1 of 1) [2271]
Over Here
Over There (contains a flashforward to 2301.)
In the Beginning (TV Movie) [2278] (The present tense of Londo as narrator is that of Londo releasing Sheridan and Delenn, and Londo & G'Kar choking each other at the end, and this has to happen between Crusade and "Sleeping in Light."
"In the Beginning" was told by Londo in ~2278.)
Sleeping in Light [2281].
[1]By then, you'll probably want to buy them all anyway.
This is a show you'll want to watch at least a few times through, start to finish. Of all of the above, there's only one thing I'd avoid, The Legend of the Rangers TV movie/pilot.