Q4 would work but it's not as popular as ETQW, by far.
For an id mod all you do is put your new content & compiled binary (dll/so) in it's own subfolder under the game's folder. Ex:
Quake4 - base
It runs the stuff in base first, then runs the mod you loaded.
Q4 has some optimizations that D3 didn't have, it also took some features out of D3. ETQW is a kind of balance between the two, but it's MP only with bots for SP.
Honestly, I'd say mod Quake 2. We're always looking for fun Q2 mods but if you want to mod Q4 go ahead, modding is one heck of a fun ride.