My budget for all monthly expense 40,000 to 50,000 THB?

You can find all the international schools in Thailand ( contacts and websites if any ) in the following link : http://www.isat.or.th/schools

You can filter by education system like american, british, chinese, german,... etc on the right side

Honestly if you rent something cheap 20K per month, plus healthcare for 3 people, plus international school you are far away over Budget.

I am not in Bangkok but in Chiang Mai i pay 200K/300K per year ( price increase easily 5% every year - 200K to start kindergarden and above 300K in last year ) and you need to pay in advance the fees by semester. This is for a british international school.

This exclude Lunch, School Bus, School Insurance, and others...

There is also a fee for 1st time registration it was 50K and there is a long waiting list 3 years in advance, that mean they ask us to pay 30K non refundable since March to book a place for our kid for next year or the place will be given to somebody in the waiting list.

I suppose you will have few choice as you did not start your homework to find a school with available place and reasonable price.

If you just need english go to bilingual Thai school, they will not follow a proper british curriculum vitae or will not be accredited by Cambridge university in the case or english education but with your Budget your choice will be limitated to this kind of school ( your kid will need to speak thai also )