The smallest SQL Server you can install for development purposes is SQL Server Express LocalDb
Microsoft SQL Server Express LocalDB is a feature of SQL Server
Express targeted to developers. It is available on SQL Server Express
with Advanced Services.
LocalDB installation copies a minimal set of files necessary to start
the SQL Server Database Engine. Once LocalDB is installed, you can
initiate a connection using a special connection string. When
connecting, the necessary SQL Server infrastructure is automatically
created and started, enabling the application to use the database
without complex configuration tasks. Developer Tools can provide
developers with a SQL Server Database Engine that lets them write and
test Transact-SQL code without having to manage a full server instance
of SQL Server.
Both LocalDB and the "regular" Express Edition have all the programmability features of Enterprise/Developer edition. The regular Express Edition installs a Windows service and is running all the time unless you stop/start the service, and is about 500MB installed. LocalDb runs only when your app is running, and is about 250MB on disk.