Would a male speaker also say "Je suis la meillure personne pour diriger le pays"?
Absolutely, either a man or a woman can be 'la meilleure personne' because the agreement is about 'la personne'.
Alexander Lukashenko, is that you?
How about "to rule the country"?
Anyone who says that is guaranteed not to be!
This is pretty funny spoken in a child's voice.
Manage the country?