Come clean completely if it's just something embarrassing and not illegal. The blackmailer will lose their power and you will appear relatively sympathetic, everyone has stuff they'd rather not get shared around and will identify with your case. Your concerns about PR are probably overblown, even if it seems like a big deal to you, most people won't think about it much

If it's something really bad, and not just an embarrassing sexual thing or something, act accordingly and realize you may have to start a new life somehow. Look into being a day laborer, for example. Hopefully you're not in that situation.

(And just in case it's child abuse or something like that, turn yourself in, and seek help, you deserve what you get)