A termination of parental rights (TPR) would be more effective. As the name suggests, the TPR would completely end all of his rights and obligations as a father. He would have no rights to custody or visitation and no obligation to pay support, he would be a legal stranger to the child.
If he did a TPR, you would want to accomplish a TPR as to the mother as well. Once both TPR's are accomplished, you could adopt.
As you can see, the TPR is a much more comprehensive avenue to pursue. It would take more time, money and effort. However, it obtains an excellent result, the children would be fully your responsibility.
A guardianship is much easier to obtain but has more limitations, primarily that it could be rescinded at any time and the children placed back with the mother, whom you indicate is NOT a good parent.
If you want the better result, pursue the TPR. If you want easier and quicker, pursue the guardianship.
Also, several customers have asked how they may direct a question to me in particular. If you specifically want me to assist you in your legal matter, just start your question with "FOR JOSEPH" and I will gladly pick up the question as soon as I am on-line.