>>On the Connect to Server dialog, click on the Options button. On the Connection properties page select database from Connect to database dropdown.
>
>That works but this setting is not saved. On the next connection, it resets to default.

I just tried it, closed SSMS, and the next time it came with my database selected.

See this, BTW
http://www.serverintellect.com/support/sqlserver/connect-database-ssmse.aspx