Started a new job after a period of unemployment. For what length of time should I work before I attempt to get mortgage approval? One month, three months, six months?

Right now would be good. As long as you show you have a job now it should be fine. Your credit score, did it suffer during unemployment, do you know you score?

Score is good.

And it may depend on the lender, if it is work in the same field, did you change jobs for promotion. It can be explained if asked
Some lenders will look at employment even up to a year, so there is no one answer for any and all lenders

What is your score?

Sorry to chime in, 750+ Score. What kind of rate can I get for 15 yrs loan (for around 75K, refi... )??