I have just come back to my home country after an intense experience in Asia, as a postdoc in China. I will give you some advice, and what I heard about India. I had originally considered India as a possible destination as well.
I do not understand much of high-school teaching, and cannot help you there.
The best scenario Asia has to offer at the moment is a combination of personal safety, delicious exotic food, and ample job opportunities. You can expect to be mesmerised daily by traditions and sudden twist in lifestyle, while enjoying an absence of violence and threats; you will get as many interesting job offers as you keep on asking.
However I recommend you to be extremely careful. I was scammed on my salary and welfare conditions by reputed Chinese institutions, as partially discussed in the link below:
Persistent issues with salary pay as a postdoc in China: What can I do?
From what I discussed with many colleagues, similar issues are common in Chinese academia, but are just not openly discussed. And a solid resistance to exposing and discussing problems is a mark of Asian culture, be it in China, Pakistan, India, Japan, which you will be quick to bump into. I heard from Indian nationals that salary scams are not common, but other issues with administration and workmates are routine. (For instance postdoc salaries in India can apparently get delayed for 2-3 months, but eventually they will come; you may expect "informal fees & favours" to get procedures done). I think most of the difficulties I've faced in China would have driven an European nuts, as the cultural impact is so deep. In short, expect to attract a lot of interests in Asia.
Furthermore I recommend you study the destination country you choose very carefully as well, in deciding the region you'll be focusing on. Like China India is such a huge and heterogeneous nation; surely your experience will heavily rely on how you adapt to local standards of where you land. I left Asia with the impression that in the long run it pays better if you focus on 2nd-tier cities instead of heading straight to the more international 1st-tier megalopolises. Expect to learn the local language from start, and complete deprivation from your comfort zone in different spheres.
Finally I warn you about the food and a different concept of hygiene. I am sure you may have heard that some regions in India have a problem with urban chaos and water safety. Almost all foreigners I have known who lived in India for more than a brief stay got seriously sick, typically from some kind of food poisoning. Many could not finally adapt to consistently spicy cuisine. I was never sick in China, and I loved the food.
I believe it will be a great, memorable experience, but I recommend all preparation and precaution you can muster beforehand.