Openarena is great. It runs like stock Quake 3, but has a few extra option like automatically switch to a new map when the frag limit is hit. It doesn't have the original bots, but they can be added if you know how pk3s work and you have the original files.
There's some configuration that has to be done, like creating a file with the map names in it, or making sure the stock mods are at the bottom of the each map sets directory, etc, but I have scripts that auto-generate configurations and symlink stock files, so I can move stuff around without thinking too much if I need to.
Protip: Nearly any Testament album will fit Quake 3. I have the music on Quake 3 set to zero. I just play my Testament playlist. I leave the sound fx on obviously.
Requires a modern source port like DarkPlaces, QuakeSpasm, or vkQuake but holy shit is it ever worth it. New enemies (that are challenging and interesting but not annoying or cringe), new weapons (like a quadruple shotgun), and absolutely massive levels that will easily take you an hour to complete.