Which eigenvector to choose after calculating PCA
The eigenvectors are in the order of explained variance. Usually one uses PCA for dimension reduction, that is, selects some N first components. The problem of choosing appropriate N is called dimension estimation. Easiest way would be to take such N that the selected PCs explain 90% or 95% of the variance in the original data. Alternatively, you could use some information-theoric method such as minimum description length (MDL).