A private lesson should be used for getting feedback about your current dancing. It often goes into technical aspects of the basics at a much deeper level than can be discussed in class and it will be specific to you.
If say you get 3 or 4 things to work on out of one private lesson, it may take months of social dancing to fix even 2 or 3 of those things.
Generally you should not use it to learn new moves. There is YouTube, DVDs and classes that are much cheaper for that.
Working on technical aspects of an example pattern that you can already do is one option but usually in the first lesson just working on the quality of basic steps, connection with your partner, the floor and timing are fundamental.
Anytime is good for a private lesson provided you remember the points and work on them when out social dancing or at class.
When you will be ready for a second private lesson depends on how quickly you need new things to work on. Sometimes only a few private lessons are necessary to put you on the right track ; so that you can work on improving yourself.
Like anything in life they're not absolutely necessary to get where you want to go but getting quality feedback early is an important step, especially if you have missed basic technique, picked up bad habits or have fundamental roadblocks in your dancing.