I'd focus on the PS3 rather than the 4. No one knows what the deal is with the controllers yet. It will take a while for an encoder to come out. It's possible the Cthulhu will already work with it if the PS4 can use PS3 controllers, or the Cthulhu could be made compatible with a future firmware update. Otherwise, you're looking at pad/other PCB hacks until something else comes along, which is doable, but why bother anyhow? It will take a few years for a new console to build up a decent library, especially if you're looking for titles that are good with arcade controls, whereas the PS3 already has a huge selection of fighters and other stuff.
Anyhow, the PS1, 2, and 3 will all output 15kHz RGB. You just need to get an RGB SCART cable, cut off the SCART end, and connect the appopriate wires to the right places on the monitor and audio inputs. The same cable will work with all three systems (well I've personally done it with PS2 and PS3, I'm assuming PS1 is the same).
BTW, be sure not to use a PS3 to play PS1 and PS2 games. The emulation causes lag, and it will always run in 480i, even if the game is supposed to be 240p. A PS2 is cheap, it's fine for PS1 games, and both PS1 and PS2 will also work with the MC Cthulhu.