Best Database to Use for iOS/Android/Web Integration

I'm looking to build an application that a user has an account for and can access their data on either iOS, Android, or web. For example, I would like every user to have one list under their account. A user would sign up, sign in, then be able to start adding items to their list. Then, they could log in on either of the three platforms and access and edit/add to their list. Is this possible? If so, what would be the best database to use, and ideally cheapest (preferably free; I saw Realm is free?). Thanks!