The Shadows could have picked any race to start a war between the races. Why choose the Centauris out of so many races? Why not help the Narns to fight Centauris instead? Or even the humans to fight the Minbaris to avenge for the Earth-Minbari war?
Because Londo answered Morden's question to their satisfaction.
The Shadow could indeed have gone with any race. As we see later in the series, the Centauri weren't even their only angle - the Earth Alliance and Psi Corps were infiltrated, and in Season Three it's mentioned that with promises from the Shadows several of the smaller holdings start wars of aggression as well.
The fact of the matter is, Londo was their first, best prospect, possibly because he simply wanted to fight for the glory, rather than any cause.
Here's two quotes from JMS, regarding why Londo was chosen:
Why Londo? Because he was the one who answered Morden's question correctly. Things happen for a reason that is suited to who the person is. G'Kar's ambitions aren't nearly big enough; Delenn knows better than to get near these guys; Kosh is against them; the EA are being kept at arm's length for now, the non-aligned worlds aren't big enough...so here we are.
There would have been more than one answer that would have sufficed, but one answer was better than all the rest. Just the right mix of resentment, nostalgia, ambition, frustration and a sense of displaced destiny. Londo was hitting all those cylinders when he answered Morden's question.
Since there been multiple requests for a reminder as to exactly how this went down, this is the scene in question where Londo answers the question. G'kars answer would also be relevant, but I can't yet find that scene online.
Do you really want to know what I want? Do you really want to know the truth? I want my people to reclaim their rightful place in the galaxy. I want to see the Centauri stretch forth their hand again and command the stars. I want a rebirth of glory. A renaissance of power. And to stop running through my life like a man too late for an appointment, afraid to look back, but to look forward. I want us to be what we used to be! I want... I want it all back. The way that it was!