How does one find and select a PhD program in Computer Science (and/or Mathematics)? How would I find and select a PhD program in Computer Science, or Computer Science combined with Mathematics? Since I am not a traditional candidate, I am unable to seek relevant advice from professors and fellow student. I am not too concerned about school ranking.

Some background about me and my circumstances may help frame the question and better focus the answer.

I have substantial experience in software engineering (over 20 years), including analysis, requirements, architecture, design, (extensive) hands-on development, testing, systems, team leadership, mentoring, management, and process. Many colleagues have said that I am really good at explaining concepts. I could continue working in software development.

I have a BS Mathematics and Computer Science minor, earned prior to my software career. And I am halfway through a MS Computer Science (part-time). Grades are solid (3.8 undergrad, 4.0 grad), the schools are good, and GRE scores are good enough (>160).

I would either return to my career or I would seek a position teaching at the college level. I am not concerned about about tenure or reputation, nor do I expect to become wealthy. I am willing to TA, and would probably enjoy it.
Since I am not a traditional candidate, I am unable to seek relevant advice from professors and fellow student. — Nonsense.  Of course you can seek relevant advice from professors and fellow students.  Yes, you're a non-traditional student, but you're not so non-traditional that "traditional" advice doesn't apply to you.

You need answers to the following questions, not necessarily in the following order:


What kind of research do you want to do? — Are you interested in doing research in algebra, algorithms, analysis (real or complex), animation, architecture, artificial intelligence,...?  Which subfield(s) of mathematics and/or computer science do you enjoy working in, and which subfields are you actually good at?  This is not the same question as "Why kind of classes you you want to take?"  A PhD is a research degree; admissions committees will be looking for your interests and potential as a researcher.  It's perfectly fine not to know precisely which subfield you want to work in, but you should at least have some explicit priorities.
Who does the kind of research you want to do? — Who are your potential advisors?  Your advisor and your other faculty mentors/collaborators have at least as big an effect on your success (and enjoyment) as a PhD student as the department you apply to.  Look for departments that have at least two or three people who are active and successful in your target subfield(s).  You don't want to find yourself in a department where nobody does what you care about, or more subtly, where only one professor does anything you care about, but the two of you don't get along for some reason.
What are other strengths and weaknesses of the departments? — Now that you know who you'd like to work with, and where those people work, other factors come into play.  How strong is the overall department?  What are the course requirements?  Given your past record (and likely recommendation letters), how likely are you to be admitted?  How likely are you to get funding?  What is the expected workload for teaching assistants?  Are there many other nontraditional students?  Again, you don't need firm answers to every question about every department, and some questions can only be answered by a physical visit after being admitted.
Can you see yourself living there for five years?  Is the department in a big city/small town?  What's the weather like?  What's the traffic like?  What are the local politics?  How good is the local food/coffee/beer?  Any good nearby farmer's markets / museums / hiking / judo / frisbee golf / hip-hop / swing dancing / fishing / rock-climbing / maker spaces / improv / underwater hockey / SCUBA / musical theater / Zen centers?  How close are your family and friends?  If you're married: Are there opportunities for your spouse?  If you have kids: How good are the schools?