How to change default security on SQL Server database so that everyone can use it?
You could create a domain group that you could use to create as login and user on your SQL Server and YourDatabase.  After creating the domain group, you could do something like:

USE [master]
GO
CREATE LOGIN [DOMAIN\AllUsersForYourDatabase] FROM WINDOWS
GO
USE [YourDatabase]
GO
CREATE USER [DOMAIN\AllUsersForYourDatabase] 
FOR LOGIN [DOMAIN\AllUsersForYourDatabase] 
GO


You can then make the logins on your domain members of that group. All the logins will inherit the permissions granted to the group that gives them access. (You could include Domain Users in the group if you truly wanted everyone in the domain to have access.) 

Of course, you need to grant the needed rights to the YourDatabase user [DOMAIN\AllUsersForYourDatabase] so that everybody in the group gets the same rights.

If you need some users to have additional rights, those can be individually granted.  Or you can create another Group that would include only the users with the extra rights.  The users will get the aggregate of all rights from all groups for that login.