I don't know if I should wait for a relationship/someone I actually care about or just fuck some random girl
Sex is better with someone you feel an emotional connection too.
That said pop your cherry however the fuck you want.
I'd recommend at least going on a date with a one night stand tho. And not just picking up some chick at bar and fucking her that night.
>How important is it who your first fuck is with?
This should be something you already know, whether you've fucked or not. If you care, then obviously you won't want to, if you don't, then you won't care.
I don't care now and I never cared and I had sex with a friend of mine who shared that sentiment so we just agreed to have our first times with one another.