Question: How Can I sort a list of polynomials with parametric coefficients based on some criteria?

Hi all,

How Can I sort a list of polynomials with parametric coefficients based on the following criteria?
1. Fewer different parameters in the coefficients.
2. If the number of parameters is the same, the lower power of the parameters.
3. If the previous criteria are the same, sentences with parametric coefficients appear later.

Otherwise, the list is in order. For example, I want to obtain the sorted list 

[(a+2)*x[1]+3*x[2]-x[3]+(a-2)*x[4],2*x[1]+2*x[2]-b*x[3]+(c+1)*x[4], (a-1)*x[1]+x[2]+(a+1)*x[3]+(C^2-1)*x[4], (a+b)*x[1]+(c-3)*x[2]+(-b-1)*x[3]+2*x[4]] from the following list:

[(a-1)*x[1]+x[2]+(a+1)*x[3]+(C^2-1)*x[4], 2*x[1]+2*x[2]-b*x[3]+(c+1)*x[4], (a+2)*x[1]+3*x[2]-x[3]+(a-2)*x[4], (a+b)*x[1]+(c-3)*x[2]+(-b-1)*x[3]+2*x[4]]. 

Could you please guide me?

Thanks.