For example the NCATE,CAEP…Regional or national accredited?
You want to attend a college or university that has regional accreditation.
Why not national
In the US higher education system, regional accredition is much more valuable than national accreditation. Regional accrditation means that your degree will be recognized everywhere, and if you transfer to a different college or university, your classes can transfer. If you go to a different country and have to have your US diploma validated for that other country, regional accreditation is necessary.
Places that aren’t good enough to qualify for regional accreditation get together and make their own organizations and call those organizations national. If your college or university only has national accreditation, you probably can’t go to grad school anywhere except for a place that has that same kind of national accreditation. If you try to transfer to a regionally accredited place, you probably will lose all of your credits.
Frankly, I can’t think of any reason to study at a nationally accredited college or university.
National accreditation is for particular disciplines: education, business, law etc. If the college overall does not qualify for regional accreditation then national accreditation is unlikely in any particular field.
Practically, there are excellent teachers and poor teachers on any campus. There may be major disagreements which faculty fall into which category. What works for one student may not work for another. Some areas are pits to some individuals. For example, who would major in business. Faculty are evaluated on research, teaching and service. Publications are typically considered more important. There have been any number of excellent teachers who were not tenured because of insufficient pages literally in research journals.
Look at the overall quality of the school, but expecting one to emphasize teaching quality, unless specifically addressed, is simply chancy.
Here is one good summary about regional vs. national accreditation for colleges and universities:
https://blog.tesu.edu/national-vs-regional-accreditation-why-does-it-matter
Except for some very specific careers that are not offered at any regionally accredited institution, you want to attend a regionally accredited college or university. As @TomSrOfBoston mentioned above, for some majors it is also important that the specific major be accredited by a national organization (e.g. http://main.abet.org/aps/Accreditedprogramsearch.aspx for engineering majors) or by a state licensing agency.