I want to implement a database solution to store animal interest forms on. Their current system of sifting through papers is janky to say the least.

Does anybody know of any cheap, preferably free or open-source, database providers I could work with? I've looked at AWS etc but they're all incredibly pricey for a non-profit organisation.

EDIT: Extra points if I can connect the database back-end to an online web form.

FURTHER EDIT: Have decided to build a local MySQL database, with regularly scheduled backups. Thinking that the online form could return JSON data that I will allow to be parsed into the database. Any thoughts further to this?