I save at the beginning of every level, and then create a separate save right before annoying fights or sections. I name them with a shortened wad name, and then the map number. I update the map number when starting a new level.
I suggest you play anything by Cyriak Harris (aka mouldy). His levels are super high quality and pretty tough. There is also a load of doomcute in his maps. I recommend Going Down for a large building of a megawad, or the recent Overboard for a short, difficult and doomcute filled 6 map vacation.
The choices are 32x, SNES, PS1, GBA, Atari Jaguar, or other (be it 3DO, Saturn, Xbox 360, etc)
My personal favorite is SNES Doom, just because it is a huge technical feat, even though it plays like garbage. Also the music is great imo.