Looking at your collection , I see no option but to get rid of the Star Trek, it is never going to fit in withe the EMs

But seriously, I'd put ST in the center of the room, either side would be Firepower and sorcerer. The EMs in any order aafter that

I am not familiar with your games so I will use other games as examples
I would not put a CV next to a scared stiff as they both have action in the back boxes
I would not put high speed next to a tomcat as they both have becons
I would not put a LOTR in a corner because it is a dark machine

A lot will depend on set up of your space. A large open room or smaller separate rooms. Group them by theme or manufacture. An older EM will really look old next to the Star Trek. Is there a single spot for the ST? It is cool if the EM pins are set up in chronological order, by manufacture, as only us pinheads would understand that. Grouped by theme may appeal to casual players that only like a certain theme. You have a good problem to solve with some pushing and shoving involved.
Good Luck.

i would have to go alphabetical.

Ditto ,on the Star Trek.

I think I would group by brand, configuration and age. I would also sell the Star Trek and buy ten wedge heads to balance out all those multiplayers and really, tie the room together.

or... you could retheme your gay 90's into a Reading Rainbow and park it next to the Star Trek.

I order them by when i bought them for the most part which ends up being their placement

-Jeff

I try to keep machines that are alike grouped together. Nothing looks worse than a modern Stern next to a wedgehead. So modern games in one room, classics in another, and then single spots around the house get machines that don't fit the mold of a room.

I started with mine in chronological order, this way the sizes and height of the games was similar...but then they outgrew that room, so now I have the early SS and EMs in one room (basement), kind of placed with my faves on one side and hubbys faves on the other...then EMs and other manufactures (we have mostly Williams early SS) on the other wall...then all the system 11s have their own room (formerly the dining room) and newer Sterns and WPCs have their own room (formerly the living room) system 9s are kinda placed wherever there is room, right now one is in the entry hall and one is on the side with hubbys faves (it is going to have to move soon cause it is in Defenders spot!!) and then the odd shaped ones, Joust and Varkon are in the family room...Hopefully getting ready to add/remodel so there will be another gameroom and they can all be together again...more room for pins!!!

Phoebe