Hey there! I can't really speak to what factors are considered to be most important in your application, as I'm a fellow applicant myself. However, I have access to the US News information on graduate schools for education, so I can provide you with some statistics on admissions.
This information is for all the Master's programs at the graduate schools of education, so keep in mind that these numbers don't just reflect the teacher education programs. But it's better than nothing, right?
USC
Applications 1,990
Acceptance rate (master's) 61.8%
Average GRE score (new test) 151 verbal, 151 quantitative
UCLA
Applications 541
Acceptance rate (master's) 67.3%
Average GRE score (new test) 152 verbal, 149 quantitative
UC Berkeley
http://gse.berkeley.edu/admissions-faqs (for all admissions to the Graduate School of Education)
Applications 365
Acceptance rate (master's) 30.7%
Average GRE score (new test) 159 verbal, 156 quantitative
Stanford
https://gse-step.stanford.edu/sites/default/files/stepfactsheet1.pdf (fact sheet for the Stanford Teacher Education Program)
Applications 983
Acceptance rate (master's) 32.2%
Average GRE score (new test) 160 verbal, 157 quantitative
UCSD
Applications 114
Acceptance rate (master's) 78.9%
Average GRE score (new test) 153 verbal, 152 quantitative
UCI
Applications 222
Acceptance rate (master's) 91.9%
Average GRE score (new test) 153 verbal, 151 quantitative
Hope this helps!