I don't think there's anything canon, but you can make a few assumptions.
I think the best assumption to make is that the most common species are those enslaved by the Hutts (Vodrans, Klatooinians, Nikto) and similar races used by the Hutts as mercenaries (Weequay).
My logic: for the slaves, I'm thinking that the Hutts would do their best to ensure a constant stream of slaves for every generation. They probably breed their slave races for many traits, and numbers would be one of them.
25,000 years of slavery should ensure a large number of Vodrans, Klatooinians, and Niktos in the Galaxy.
Twi'leks would apply similarly. Twi'lek slavery is common (not just for the women), and so a slave population might be bred to maximize their numbers.
The same logic might apply to the hired races, but from a free will point of view. Each family is well off working for the Hutts, so they make sure there's enough in the next generation to serve further.
But that's just a thought.
It was the year of fire… the year of destruction… the year we took back what was ours.
It was the year of rebirth… the year of great sadness… the year of pain… and the year of joy.
It was a new age. It was the end of history. It was the year everything changed.
The year is 2261.
The place: Babylon 5.