I am not serial killer and I even do not have any interest in that but if i had to be I would be more focused on publicity like zodiac killer.

I woud go after famous people or at least those who are somewhat known or could spark interest of from society or small groups.
I would do executions or torture in public releasing all footage on internet. My preferred method woud be to force other people into doing all job, somewhat similar way as in "euphoria" game/anime, since I can't go into public myself. Even if I get caught then I can say that I was just a victim LOL.
Ideally, I woud prefer not to kill anyone, but play with them giving chance to escape without even getting permanent damage.
(this also places some requirements on target selection because I don't want my victim to get petrified and spending all time begging to spare her life)