Of the three you chose, I prefer Alexis for a middle name, but Alexa for a first name. Alexa is slightly softer and easier to say, and would be less likely to be shortened to Alex or Lexi, but for a middle name, Alexa would sound like a cop out; Alexis would be a more sophisticated choice (I think).
My favourite Alex name is Alexandra, but only as it is pronounced in Europe - aleks-AH-ndra. That pronunciation is absolutely beautiful; alegz-ANN-dra is not. But in an English speaking country, people would always pronounce it the second way.
There is one Alexandra I know of in my social circle.