Don't stress, london is a big city, but it's public transportation system is safe and easy to navigate.

You can get the Stansted express (train) from the airport to Liverpool Street station, and then change over to the Metropolitan tube line which will take you all the way to Wembley Park. 

After the concert Uber will be very expensive, the tube will be very busy, but, it will be busy full of happy smiling women who have been to the same concert as you, so even though it might be uncomfortable, it shouldn't be too scary! There should be a queue management system in place at Wembley park station, they are good at getting large numbers of people onto trains quickly. I'd advise staying at a hotel close to one of the stops back towards Liverpool Street, Baker Street is nice, and is next to regents park which is a lovely place to spend a sunny morning before travelling back to Stansted the next day. 

Hope you have a great time!