SQL Server: What securables to enable a server role for read-write access to all DBs In SQL Server, you can add a server role and give that role membership to other roles such as:


bulkadmin
dbcreator
diskadmin
processadmin
securityadmin
serveradmin
setupadmin
superadmin


However none of these roles seem to allow for only interacting with databases (SELECT, INSERT, UPDATE).

What securables should I enable to specifically allow for this kind of access? I would not want this server role to be able to create and drop databases.
To give access to a database you need to use database roles and database users but not server roles.  Please check difference between a user and a login

You can create a server role, add logins to that. Then you can add that role as a user in each database and add it as a member of a database role that has select, insert and update rights. 

If you do this in the model database and then that would be copied to all user databases created after that.