The manual is a little vague on many points so really playing any of the factions is a little daunting at first. There a multple wiki pages on SOASE but this one is my favorite.
https://www.sinsofasolarempire.wikia.com/wiki/Main_Page
You can read about the factions in more detail and also see them contrasted in various data tables.
I usually play the TEK but just played the single-player multi-star (5) game as Vasari. I stumbled around a bit as I was not used to the ships or tech trees but I still won the game and had fun.
My favorite Vasari feature is the ability to travel between any two planets in a solar system, regardless of phase lanes! There are 2 ways to do this. One, research the phase stablizer (I think that's the name) technonolgy and build such a node at each planet you own; it is on the tactical menu of a planet. But there is also a capitol ship that can do the same thing on the fly no matter where you are! One of the fancy capitol ships can gain the ability to create a phase stabilizer node where it sits! It lasts for about 70 seconds or until you 1st use it. Drop a node with one of these ships at one planet. Drop a node with one of these ships at another planet. Select the ships you wish to transfer directly between these two planets as you normally would but now they'll make the jump directly, just as if a phase lane existed there! It is fun, give it a try!
It is so cool to be able to instantly pop your fleet anywhere.
Also, have fun with the mega weapon. It hits the orbital structures of an enemy planet; good for softening up a planet prior to attack!
The Vasari may become my new favorite faction!