I have been wanting to play the original DOOM 1 and 2 but I am not sure what's a good way to experience it proper.
I know about UZdoom but I hear it changes things that affect the original gameplay. There's also just playing the re-release version but not sure how optimal it is. I am also open for QoL mods like visibility/eye-strain stuff.
The original Boom was (only ever) published for DOS. Active development ended in 1999. The thing which makes it notable is that it was the first 3rd-party source port to add new map design features (quite a number of them, too). You almost certainly don't want to use Boom today unless you are in a true retro-computing mood and are prepared to bust out DosBox or a PC emulator (the requirements are essentially identical to running the vanilla Doom binaries).
The good news is that Boom came out and stabilized so early that it effectively became a defacto standard. Many, many custom levels are developed with Boom-compatibility as a target (even today), and nearly all modern source ports support these maps (with the deliberate exception of Chocolate Doom).
There is also a lineage of ports which descend from Boom, like DSDA-Doom by way of PrBoom+, or even the official engine which ships with "Doom + Doom II." Even modern ports which can't trace their heritage back to Boom will typically include snippets of code from it for one reason or another.