Just my two cents here, take it with a grain of salt.
My gut reaction is to suggest the most popular games. Pac-Man, Ms. Pac-Man, Galaga. The most widely known games will be the most plentiful, and also have the most available replacement parts. But on the flip side, they're the most recognizable and people have already come to understand that, and therefore the prices have gone up. Even moreso now that arcade bars have become a thing.
Maybe it just comes down to passion. What's your favorite game? I first had an Gyruss cabinet but have ended up with a Star Wars machine (which needs some serious rehab due to an unfortunate dolly accident during moving). Personally, it's my plan to fix the Star Wars machine, and with that said, anyone have any suggestions for mitigating cracks in the MDF of a cabinet's side without sacrificing the side art?
Really good question - original cabinet games are so hard to find and are normally in the $500 to $1000 range if you want all the same existing hardware and monitors. And it is not guaranteed that it will work. Check out Mike at The Geek Pub and build one of your own! He shows you how to do it on the cheap with a raspberry PI! I am in the process of tackling this project myself and will be starting the cabinet this week.
Any one that you can pickup locally? Personally, if you are going through the effort of finding and doing a restoration, I would pick a personal favorite, something you want to show off in the playroom. For me, that would be Galaga for something older and Golden Axe for something a bit newer.
For ideas, maybe look at Johns Arcade on youtube. He has a full blown arcade in his basement with many popular games. Most of his picks I believe are from Craigslist, auctions, trading with other collectors, etc. He also has several restoration videos and arcade game "pick-up" videos.
BTW, I wrestled with this a bit myself and was originally leaning towards doing a build and even bought the plans from Mike at the Geek Pub. I ultimately went with a cabinet from RecRoomMasters. A bit pricey but I was able to assemble in a few hours, it looked professional, and the cabinet is made with melamine which has a much better finish than the MDF I would have used. Additionally, I have a completed arcade machine rather than an unfinished project sitting in my garage. It's certainly not as authentic as an actual arcade machine but worked for me.