When you start you get a credit for appengine, in my case it was 200USD which will be enough for your campain.
If you use App-Engine and have data that contains private information like date of birth or full names, you can use a GSuite Account to run the Database.
This would be the highest monthly cost you have except you get GSuite as an organization for free.
Alternative is to use Amanzons AWS... as a NGO you can get 2000USD per year in credits:
http://www.techsoup.org/products/amazon-web-services-credits-for-nonprofits-(boost)--G-50221--