Whenever possible charge for results not your time.
Base your rate on the value you will be providing your client. The bigger the problem the bigger the fees. If you can make the pain go away they will gladly pay you.
It will take far longer than you think to begin generating a decent income. Figure a minimum one year probably closer to two. Plan accordingly and don't give up.
Remember you are low on a very long list of worries your client has. Don't take it personally. Continue to be friendly and responsive even if you don't get the same courtesy in return.
Provide a report or have a conversation with your client before submitting an invoice. Make sure they know the value you have provided and are prepared to pay.