How do you measure the outcomes of general education (up to 12th grade) and higher education (college and above) in a given country? what are some indicators you would suggest I use?
Outcomes can vary significantly among different countries. I'd say you would need to start with the specific country's evaluation system, and then move from there.
What outcomes are important to you? To decision- or policy-makers? To the general public? To educators? To your specific research questions? Are you trying to emulate an existing study with new/different sites? If so, what outcome(s) did the authors use?
There are so many possibilities, but, Nicolo's reply hints at something very important: What sorts of indicators are available for the site(s) you propose to investigate? You obviously can't use what isn't available.
To choose just one outcome, academic achievement, do you rely on: (a) state or government test scores, (b) national indicators (such as NAEP), (c) international indicators (such as PISA), (d) graduation rate, (e) proportion of graduates attending post-secondary or professional schools, (f) employment status 6 months after leaving school, (g) lifetime earnings, or something else? All of these have been used, and they can yield dramatically different pictures of an institution's success.
Try looking at some recent studies in high-impact journals; which ones sound most like they are addressing the kinds of questions you'd like to be able to answer. That would be a good start. As well, I'll bet your college has several knowledgeable folks who could help you narrow down your search.
Outcomes can be measured if the learners file for a patent pending, a trademark, or a copyright. This is if the outcomes are practical. If the learner graduates and attends a prestigious university - this may also count as an outcome. Back in the day, outcomes were measured by a question, "Did the person become a Renaissance man or woman?" Thank you.
You need to consider the alignment of general and higher education competencies (soft, technical and professional knowledge and skills), the country's priorities for education and labor force preparedness, which should be aligned also to global trends and country's future vision.