Equal or Unequal Samples when comparing more than two means? Does that matter?

#1
I am going to conduct a study in which I'm going to analyse the mathematical performance of indigenous students in school A and will be compared to non-indigenous students in public-urban (school B), private-urban (school C), public-rural (school D) and private-rural (school E) schools to determine if the performance of the indigenous students is at par to those non-indigenous students in different school settings. The data will be gathered through a standardized test. All students are of the same grade level. The total number of indigenous students at school A is 23 and I plan to include them all in my study. On the other hand, the total number of non-indigenous grade 10 students in school B is 1750, school C is 200, school D is 150 and school E is 80. However, I don’t have enough time and resources to include all students in schools B, C, D and E so I’ll just take a sample from each. Do I have to take sample from the schools B, C, D and E separately, yielding different number of subjects in the 4 school types? Or I’ll make the sample size equal of 23 in all schools (A, B, C, D, E)? I’ve seen a similar study of mine http://www.hrpub.org/download/20160130/UJER2-19504845.pdf wherein in the table 2, the comparison of the performance of the indigenous students to the school types, the number of indigenous students is 18 and number of students in each school types is 20. I don’t know why the researcher chose 20 for each school types and I think that the researcher chose 20 because it is closer to 18. Can you cite references if you don’t mind? Thank you for your time.