Databases hold critical data of an organization. Therefore the cloud infrastructure needs to take care of its storage, CPU, RAM, network, security, licenses, data protection, and backup.
Following are the points that you need to consider while hosting databases in the cloud :
(1) The database on cloud works on the PaaS model. In the PaaS model, the public cloud provider offers you a managed database service which is also called as Database-as-a-Service(DBaaS). In this service most of the administrative tasks including backup, patching, setting up an infrastructure, providing SLA backed availability and scaling up and down of data is handled by a cloud provider.
(2) To ensure the smooth working of the business, it is important that you consider setting up your DBaaS in Multi-AZ setup.
(3) While running databases in the cloud you must ensure that the cloud service protects your data from other tenants and external attacks.
These are the basic points that you should consider on a primary basis.