So, PSX mods work by injecting a 4-letter region code during boot, the first screen, right before it goes to the black secondary boot screen. For NTSC-U, like my (SCPH-9001, PU-23) PSX, that code is 'SCEA'. That's it. This code was burned into retail discs using factory equipment; home burners cannot replicate such in the inner ring.
My first mod method was to buy a PS-X-Change v2. It's a basic swap disc with a brass springed mechanism to hold the open tray sensor button down. It worked great, but was a pain because swapping and taking longer to get to playing.

Later, got my first modchip, an OLD sort that was cheap, on a simple PIC. It was my first time touching a soldering iron. Not (completely) awful for not using a bit of flux, heh. The chip worked perfectly for almost all games, but anti-mod games made the anti-piracy message show. Metal Gear Solid Integral, among others, required using a seperate boot disc and game genie style code to bypass the protection.
I just recently decided to update the mod to a new chip, one that uses the new(er) PsNee open-source firmware. It can be flashed to a very inexpensive arduino clone, and there are several models to choose from. I chose a NANO, as it has a built-in LED set, is like 2 bucks, and because the bottom right corner of the console is all empty space where it can live. When it injects the region code, an amber LED lights up and can be seen out of the front air slots. Install is 6 wires, since I don't require any bios patching like a Japanese console would. Works great on everything.

You may have noticed the spindle area of the laser assembly above has some tabs missing, 2 of them. So sometimes if a disc starts spinning quickly without ramping up, it'll just not grip the CD and not read. So I ended up replacing the whole assembly with a KSM 440-BAM model that a PSOne uses. It just required getting an extra extension cable. Working great, no complaints. Buying from Aliexpress seems to be hit or miss, but I got a good one.
I've got some extra spindle plate assemblies and a 1.5mm spacer (veroboard) coming so that I can fix the old drive and keep as a spare. The veroboard serves to act like a barrier to keep from pushing it down farther than 1.5-1.6mm from the motor 'deck', as this is the optimal factory spacing specified in the (leaked) PSX service manual(s). *nods*