Mysql – Organizing and assigning privileges to multiple objects in MySQL

Regarding providing DBA access, you might be better-off creating an Active Directory group and adding the DBAs into that group. That way, you can provide group-level permissions and give sysadmin to the group rather than individual users, meaning that when a DBA leaves (or a new one gets hired), you just need to adjust Active Directory rights rather than going into each SQL Server and altering logins. The same applies (though without granting sysadmin!) for other groups of internal users. Windows authentication is more secure than SQL authentication, and if you can use it, you probably should.

Regarding auditing, you can still have individual-level auditing when users are in a group. You can use SUSER_NAME() to get the username in whatever process you're going to use to log activity. Note that somebody could do an EXECUTE AS to switch their user context, but you should be able to log that as well as the IP address from which the query came, so you'd still be able to correlate activity to a person.

The idea of using a jumpstation (in your case, you mentioned a server) is possible. It would make administration a bit easier, especially if the laptop domain does not have a full trust relationship with the domain upon which the SQL Server instances are located. It would probably be a bit annoying for the support personnel, honestly, but if you go that route, I'd recommend a virtualized desktop for each IT support team member. That way, they don't have to deal with server contention issues and you can minimize the pain. If you do go down that route, then the IT support team members could have domain accounts and you'd create relevant Windows groups the same way as the DBA group.

I've done this a couple of weeks ago - Created LOGIN, ROLE and USER. Added USER to ROLE and granted explicit permissions to the ROLE itself. The advantage in my opinion is, that you can add further users later on without the struggle to grant the permissions, again.

First I created the login:

IF NOT EXISTS 
( 
  SELECT 
    "name" 
  FROM 
    "master"."dbo"."syslogins" 
  WHERE 
    "name" = 'your_login'
)
BEGIN 
  CREATE LOGIN your_login WITH PASSWORD = 'your_password', CHECK_POLICY = OFF; 
END

I've added the CHECK_POLICY param because things are created on user interaction and I'm not able to see, if policies are activated server-sided.

Followed by the user:

IF NOT EXISTS 
( 
  SELECT 
    1 
  FROM 
    "sys"."database_principals" 
  WHERE 
    "name" = N'your_username'
)
BEGIN 
  CREATE USER your_username FOR LOGIN your_login;
END

And the role third:

IF NOT EXISTS 
( 
  SELECT 
    1 
  FROM 
    "sys"."database_principals" 
  WHERE
    "name" = N'your_role_name'  
)
BEGIN
  CREATE ROLE "your_role_name"; 
END

Finally I added the user to the created role:

EXECUTE sp_addrolemember N'your_role_name', N'your_username';

After that, permissions can be set for each type of object, eg

GRANT EXECUTE ON "dbo"."your_sproc" TO your_role_name;

You don't have to add denydatareader or else, if you explicitly grant permissions to the specific objects. Beware that an for example INSERT permission doesn't include the SELECT permission on the same object. ( at least in my case it didn't ;) )

If you have problems executing or selecting from your UDF, check if you have granted all permissions on the referenced objects in the UDF itself!

Update after Cobus' update in OP:

I've executed the queries you provided based on my initial answer, results following:

select * from dbo.testtable 

-- The SELECT permission was denied on the object 'testtable', database 'xyz', schema 'dbo'.

update dbo.testtable set id = 4 where id = 2

-- The SELECT permission was denied on the object 'testtable', database 'xyz', schema 'dbo'. -- The UPDATE permission was denied on the object 'testtable', database 'xyz', schema 'dbo'.

update dbo.testtable set id = 4

-- The INSERT permission was denied on the object 'testtable', database 'xyz', schema 'dbo'.

insert into dbo.testtable (id) values (5)

-- The INSERT permission was denied on the object 'testtable', database 'xyz', schema 'dbo'.

It behaves as intended. Do you have any further permissions granted / set or properties which allow you to access dbo-schema?