The error you posted has nothing to do with users or passwords, it says it can't make a connection to the server.
So either you don't have SQL Server installed on localhost or you have it installed but it is using a named instance and you need to add the instance name as part of the connection string.
For example, by default when you install SQL Express it uses an instance name "SQLExpress" so you need servername\instancename
You should use a connection string in the format suggested
When you create the db user you must use a password that meets the default password strength required by SQL Express, an example of a password that meets the criteria is $Secret123 it has at least one special char at least one upper at least one lower and at least one numeric and meets the minium length required.
Hope it helps,