I can't recruit admirals, generals, etc. Why?
I Have the gold and the tradition for both but there is no option, not even for conquistadors and explorers
If you choose the "event" option, you lose the ability to recruit. And there are no events given in vanilla, so it's either/or. You have to either make your own, or use ones from an existing mod. Rex Maris, Death and Taxes, and Terra Nova, all have leader-generating events. You don't have to adopt the entire mod; just DL it and copy the appropriate events to your mod folder. (Also include the event modifiers, as they mostly are involved in making the events work, plus the localisations.)
Actually, I know that my events and Darken's are compatible with the standard leader-hiring methods. And I'm 99.9% certain lukew's are too.
If you don't want to use a mod, then your choice of "by event" is the worst possible, as it is equivalent to saying "no leaders, period." If that's what you've done, edit the save back to the normal option, or restart.