The rankings of the schools in Gautam Buddha Nagar(Noida) would help you and the family to arrive at a good choice.
A. The 2018 school ranking was based on a survey focussing on infrastructure, quality of teachers extracurricular activities, academic performance and overall well-balanced approach to education.
Among the list that you have enclosed
1)Kothari International School - is placed at 9th in 2018. It has the good infrastructure needed for good overall development (http://www.kotharischool.edu.in/webpage.aspx?Id=17)
2)Sapphire International School. (http://www.sapphireschool.in/sr-secondary-noida/about-us.php#call5)
3)DPS Gautam Buddha Nagar in Sector 132 - ranked 16th in 2018 (http://dps-gbn.org/infrastructure)
4)Gyanshree School in Sector 127 (please see B)
5)Somerville International School in Sector 132 This link gives you the infrastructure(http://somervilleinternational.in/infrastructure.aspx)
6)Ramagya School- ranked 10th (please see B)
7)GD Goenka Global School - this school is ranked 7th among the list of schools in Greater Noida
Further details can be sought in the following
b.Please check the schools in this list (https://schoolwiser.com/blog/top-schools-in-noida-2016-ranking), it gives a brief summary about the schools and the facilities.
c.Also browse through the Top C-Fore school survery of 2016 which figures
Read the below as points scored in each category against the schools mentioned in your list
Name Total Faculty Academics Infrastructure
Gyanshree 1116/1500 151/200 81/100 89/100
Sommerville 1134/1500 160/200 85/100 N/A
B.The Forbes Marquee India edition lists great Indian schools as per the ratings in great place to study (https://greatplacetostudy.org/school-listing).
The ratings are based on
c.life on campus
Among this list, the Ramagya school(6th on your list) features in the 2018 list with a score of 3/5.(https://greatplacetostudy.org/school-listing).
Gyanshree school (4th on your list) was listed in the 2017 Forbes India great place to study list. It also figured at 4th out of 26 in Noida top schools, stood 5th among the top 10 Indian schools for infrastructure.
With the above information, I would suggest you to visit the school websites, check out the top four ( Likely to be 1,4,5,6 from your list), then visit the schools, speak to the teachers, parents and then make take a good decision.