You can surely build up your own school website, as nowadays, GoDaddy and other sites are having in-built apps that help you design one. As you said you are not aware of how to get the domain and hosting, but this information you can get online. There are many "How to..." articles you will find to setup your website after buying hosting and domain. The usual companies from where most Indian bloggers buy their domains is GoDaddy or BigRock. When you go to buy their services, make sure you search for coupons codes. Usually, for the first year, the prices are quite cheap. Only later on, you will have to pay full price.
The other thing coming in your way is the technicalities. That will restrict the functionalities of your website and won't give you the desired effect for the way in which you want it. For example, setting up, emails, online forms, loading content updates will pose a problem for you.
If you think the price the website developers are asking is too high, let me enlighten you, that you can get it done in much cheaper rates - in as good rates as 3500 INR and even below. You can even post your requirement on Facebook groups and state your budget if you have any. There you won't have to spend a penny to get in touch with several website designers, and you can choose the one which suits your budget. You can also look at some Freelancer websites for hiring people.