Lighting is primary. Consider what you want the space to look like. Is it an acade with glow carpet and black lights and neon? How can you achieve that... what about when you want to work on games (clean, polish, initial diagnosis). Will you have enough lighting to do that without needing to drag around a light?
I finished my game room (mostly) and went with LED strip lights in a light try that sits about 9 inches down from the ceiling and the led point at the ceiling. Thats fully RGB tunable/dimmable so I can change look/feel of room in 1 second. Then I put cans in the ceiling that are purposely over the games and ran dimmer switches with LED bulbs. That works great as I turn them on low to play- glare is non existant and it provides just a little extra light to see the game if the room is darker. I can crank those up and then have enough direct light to take a good look at a game for a quick service or repair.
Finally- power... multiple dedicated circuits. I went with an outlet on the wall for every other game with a few extras thrown in. Since my games are along a wall that works and tidy cords look fine (barely noticeable). Consider floor outlets for middle of room location but also consider that doing so locks in game orientation and location so think it all the way through. Celing outlets work but I fee like I see that more than a tidy cord running to a floor outlet thats exactly where the game back is sitting.
Also- I would seriously consider chopping that larger space into three rooms. An arcade big enough to hold your largest collection- a shop big enough to work on more than just games- and another unfinished space planned so you can either use it down the line or expand some other room into it. Ideally that undinished space abuts the rooms you may expand in the future. I feel like its soooo big that it may look really really empty unless your going to grow big fast. So plan a proportionatley sized room- thats all.