It seems like your customer has opted for the standalone DB install. If you are having problems there, why not try to get the SCS service install wizard to get it to create the DB on the fly? If it is windows authentication to the DB that they're after, that is still possible if you go through the custom install path in SCS 5.0 - you DON'T have to use the standalone script. Make sure the Windows Logged in User that is running the SCS install wizard must be have permissions to create a DB on the SQL instance you are pointing to.
Specifically to your question regarding which user - you want access to the DB to be done by the account that is running the IIS services. You don't need to add any more users. If you want to control users that are allowed to access the DB through the SCS Console, then you'll define them in the SCS Console Users.