You can't just download the emulator; you need to find the BIOS for the two systems (as well as for Saturn, Dreamcast, GameCube, etc), which is not readily available unless you're on Soulseek or, probably, a Google search for "PS2 BIOS download". I don't *think* your computer can catch AIDS from messing with this stuff as it's not an executable file (but just to be safe, download them from a trusted source). Then you've just got to do the settings and download your games -- the PS2 library takes up about a terabyte (use torrents). The entire Atari 2600 library is something like a megabyte, maybe one-and-a-half. Most of the games are 4kb; the average PS2 game is about a gigabyte.
I have all the N64 and GameCube games, too, but I'd have to buy their quirky controllers (the N64 actually maps really well to an Xbox-type controller, only with the A, B, and C buttons all on one side.) .
Speaking of AIDS, it's almost time for this holiday classic:
It's funny to see people talk about the PS1. It was always PSX until late in the system's life, when Sony put out the PS1; it was a cheaper unit, like the top-loader NES, and I guess with the proliferation of PS2, PS3, PS4, and PS5, it's only natural to retcon the PSX. But I won't budge -- I refuse to call the first Star Wars movie "A New Hope" for the same reason. I don't know what the X stood for in PSX