Los Angeles - Public Defender or Private Criminal Defense Attorney

For 288.4 (b) in Los Angeles, CA is going the public defender route recommended or not? I’m not sure of the situation but I was shocked when I called the jail and heard the charge. Im trying to arrange things while the person is in jail for the next week awaiting arraignment. Private attorneys obviously come with high costs and to be honest I don’t have parents and money is tight but they’d at least be able to speak with the person before the arraignment.