Okay, My observations right off the bat, Mechwarrior and Gundam Wing would have to have a merger, otherwise Gundam Loses out by sheer numbers. The general technology levels from Battletech are several times more advanced than what was seen in Gundam, IE you have things like the FTL Jumpships, Black Box Communication Units, and the ability to manufacture serious amounts of mecha.
The territory claimed by humans is likewise huge compared to Gundam. That largely happened in the Sol system, with the main three planets being earth, mars, Jupiter, and associated moons, with several orbital platforms. Whereas in Battletech/Mechwarrior, you have hundreds of star systems colonized and claimed by humanity.
In terms of Mechs, Gundam Wing's have a far superior edge in combat ability and or agility. IE, the main differences between the "Super Robot" and "Real Robot" Genres.
Phantasy Star, I am assuming you mean the Sega Genesis RPGs. Its not impossible to have those characters in a mecha based storyline, But my instincts are telling me that all of the reality that the characters experience would be housed on a hyper advanced computer system, with them all existing as programs and software, similar to a holodeck in the later renditions of "Star Trek"
(I could be wrong on this.)
Those three could mesh easily well, using either Mekton-Z as a system, or even GURPS.
The other Genres you named, I am not familiar with, I would have to do some research and get back to you.