"Why do I need to choose first 2 column"

When we put a matrix in echelon form there are 2 types of column - Pivot columns and non-pivot columns

Pivot columns are the ones with the leading entry of a row (the first non-zero entry of a row).

The pivot columns are underlined in red in the picture above.

These correspond with the linearly independent columns of the original matrix so we choose them to make a basis.

You can confirm that for the matrix, A, we have,

-(3/2)*[1,0,1] + (1/2)*[1,2,3] = [-1,1,0]