I Have Taken a Solemn Vow to Never Again Get Into a Currently Airing TV Series. Hence...
My conclusion, based on limited information, is that the President was assassinated by the Home Guard.
Here's a list of the usual suspects:
None of the alien powers had a motive to assassinate the Earth President. Narn and Centauri were squabbling over Sector 37, the M'bari seem to like the humans and the Vorlons have no motive whatsoever. (Also, the Vorlon response when they see something they don't like is to obliterate it with overwhelming force, not to stage an explosion. See: Deathwalker. See also: series premiere.)
Earthforce Military: It doesn't seem like their style. The off-station Earthforce personnel we've met have individually been jerks (the captain of the cruiser in "A Voice in the Wilderness", the girl with a grudge against Garibaldi, the guy who assumed control of Babylon 5), but collectively, they haven't seemed evil in any serious way. And they, too, have no motive to do the assassination. Meanwhile, we've heard some talk about PsyCorps controlling the government behind the scenes, but if they control the government, why assassinate the head of it? It doesn't make sense, and we don't really know enough about those claims to be sure of anything.
The Home Guard are the only people who have a distinct motive. In "Chrysalis", the newscaster said that the President was due to give a speech on human-alien policy for the rest of his term. The Home Guard movement grew up in the first place because people thought he was giving aliens too much freedom. Now, he's dead and the more conservative Vice President is in charge. The VP's first speech as President was very pro-human and anti-alien. Thus, the Home Guard movement had a motive to kill off the alien-friendly President and put him in charge. We saw their means (the crates of equipment) and we know that they have recruited people in Earthforce, which could've been how they did the dirty deed.
There's a conjectural argument in favor of the Home Guard as well. We learned during the episode that crates of the equipment used to kill the President--frequency jammers and things like that--came through Babylon 5. There was no obvious motive given in the episode for this. We don't know where the equipment was being shipped from or why it had to stop at B5, but on the surface, there doesn't appear to be a reason why the conspirators had to risk discovery with an unnecessary stop.
My theory is that the crate of parts Garibaldi found was left behind apurpose. I think they were meant to be found after the assassination (which is why the man shot Garibaldi; he found them too soon and could have prevented the assassination if he'd gotten word out). The conspirators made the extra stop and left the parts behind because they wanted a trail leading to B5. Why? If it's the Home Guard, they would want to give the new President a mandate to throw suspicion on or take action against the major alien powers. So they left the crates on B5, the one place where almost every type of alien species congregates, with the idea that when they were found, suspicion would fall on the aliens. This theory allows for the new President being a part of the HG (to give him an excuse to take action) or being innocent (to push him into action).
Other Business: Londo's 'Good Fortune'
So, the mysterious Helper Man returns again, and this time he destroys an entire Narn military base to help out Londo. This is done, as revealed by the conversation at the end of the episode, to help put Londo in a position of greater power so that the Mysterious Black Spiky Guys can call on him when the time is right. (Why would a species design their ships in their own image? Does the Space Shuttle look like John F. Kennedy and I just didn't notice?) Technology-wise, these guys are clearly in a different league than everyone else (except possibly the Vorlons and the Guy on the Planet Below). They have cloaking devices and energy beams, as opposed to firing shots of energy; they are the New England Patriots to everyone else's Wisconsin Badgers at this point.
The M'bari have some idea who they are; Dillenne recognized Helper Man when he called on her before. The Vorlons know who they are, because the guy didn't go see Ambassador Koch, and the Vorlons know everything. It's not unlikely that the huge threat that each of those two races has been warning about starts with the MBSGs. What they want is unclear, except that it involves the Centauri. Maybe they're the threat that future-Sinclair needed B4 as a base to fight, maybe they're the unseen threat that Garibaldi fought in the flash-forward, maybe they're the reason the Centauri seer saw Babylon 5 possibly exploding in the future. At this point, all of this is guesswork, because we know nothing about who they are and what they might want.
I'm not sure why Garibaldi's acting was so wooden in this episode, why they threw in the random marriage between Sinclair and whatshername, or why Garibaldi was left with "50-50 odds of survival" when we have a flash-forward that shows him alive and fighting in the future.
There's also the business of the Chrysalis, and the first real M'bari-Vorlon connection.