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many different ways; depends on the workflows, versioning/reconcile/post and authentication options in use
You can see the database connection best practices on my community.esri.com blog.
You can use a domain account to run the ArcGIS Server Windows Service and add the same domain account in the SQL Server database and grant read-write access.
I recommend to not use the domain account to own data in the SQL Server Geodatabase.
For more best practices see my Production Mapping database guide book for SQL Server in the link below.
Mapping and Charting Solutions (MCS) Enterprise Databases Best Practices
I hope this helps.