I would recommend both, but doing passport first makes sense, as it is quicker and it seems your case is pretty clear. You can actually do both concurrently, as for N-600 you will only need photocopy of your father's certificate and other documents.
If your case was dubious I would probably recommend the certificate first as USCIS will do a more thorough job of making sure that you are a citizen, and they can't come back and tell one later on that one applied for a passport when one was not a citizen.
Passport takes about 3 or 4 weeks and certificate will take around 5 or 6 months. If you're applying for a federal job you'll get the proof of citizenship quicker with the passport. It seems that in certain jobs they insist on certificate of citizenship, but most likely passport will be enough to apply for the job.
If your case was dubious I would probably recommend the certificate first as USCIS will do a more thorough job of making sure that you are a citizen, and they can't come back and tell one later on that one applied for a passport when one was not a citizen.
Passport takes about 3 or 4 weeks and certificate will take around 5 or 6 months. If you're applying for a federal job you'll get the proof of citizenship quicker with the passport. It seems that in certain jobs they insist on certificate of citizenship, but most likely passport will be enough to apply for the job.