Farscape is also excellent, and I ran that for a while too.
We're playing IRL. My groups tend to be a mix of "I've watched the series at least once" and "I have not ever seen that, but a person is running it so I'm willing to play."
There are multiple options on when to set it. I've done post-Crusade, post-Legend of the Rangers but pre-Crusade, and the current one is set during season 1. The players are able to completely throw off the plot of the series, if they do something that changes things.
For Telepaths, your P-Rating is fixed at first level. I'm not sure how first edition did it, but second edition it's a 2d6-2 roll, and if you take the telepath class you can optionally add +6 to it, or get a bonus telepathy feat (I've never seen anyone take the bonus feat). Second edition gives you access to all normal abilities, but they have a base Power to use. Your power is your P-Rating + effort put into using the ability, with a maximum of +6. You then take non-lethal damage of Xd4, with X being the number you raised your effort for.
There are some guidelines for telepathic experiments, but Vorlon experiments aren't covered as thoroughly. You can kind of make that one up as you go along, since Vorlons could give a person gills or create telepaths in a race that didn't previously without much issue.
Base races and their ability score adjustments:
Humans: None. Same D&D 3.0/3.5 bonuses.
Abbai: -2 Strength, +2 Wisdom
Brakiri: None
Centauri: -2 Wisdom, +2 Charisma
Drazi: +2 Strength, -2 Intelligence
Minbari: +2 Strength, -2 Charisma
Narn: +2 Constitution, -2 Charisma
Pak'ma'ra: -2 Dexterity, +4 Constitution, -2 Charisma
First edition did attempt to make Vorlons and Shadows playable, but it's best done in specific campaigns. Here are there stat bonuses:
Vorlons: +10 strength, +10 Dexterity, +10 constitution, +10 intelligence, +2 wisdom.
Shadows: +12 strength, +6 dexterity, +10 constitution, +12 Intelligence, -2 charisma.
Second edition only gave Kosh Influence as a stat (I'll mention Influence more later.
There are rules for Technomages too. They don't have spell levels, but lots of spells have prerequisites. Fireball (whatever they call the Technomage equivalent) requires at least Create Flame (palm-sized fire), Control Flame (manipulate a single flame), Create Conflagration, and Control Conflagration.
Babylon 5 characters are squishy! You only get a normal amount of HP (5-8 plus con bonus) at first level. After that you gain 1-3 HP per level, with no con bonus or penalty.
Influence is one of my favorite things about the Babylon 5 system. It represents your ability to grease the wheels or call in favors to get things done. With a little influence, you can get an investment in a project or access to records. With a lot of influence, you can start a war, get access to the deepest of secrets or gain the use of the most powerful warships. It's divided into categories for local influence, ranging in size from a solar system to a city, special influences like criminal influence, and influence with the various races. Race influence is divided into categories, Economic, Military, Social, and Political.
If you don't have the exact influence you need, most groups can put pressure on other groups to get what you need. Any Earth influence can pressure any other Earth influence, and any Political influence can pressure any other Political influence, but it's easier to do something directly.
I'm currently running the Fiery Trial module, and since I don't have many players everyone is playing gestalt characters from the D&D 3.5 Unearthed Arcana rules.
One is a Drazi Agent/Trader, that uses his trader background as a cover for any illicit activities. The agent is basically the 3.5 Rogue with a name change, and trader is custom for Babylon 5.
The other is a Human Telepath/Soldier (reskinned Fighter), loyal to Psi Corps and connected to their seedy underbelly.
And for some non-Babylon 5 commentary: A good roleplay could be fun.