What should I monitor on the SQL Server machine?
Some of the options you mention (file auto grow for example) are already logged in the SQL Server default trace http://msdn.microsoft.com/en-us/library/ms175513.aspx

Other options for your own monitoring can be done via windows perfmon to monitor all kind of windows or SQL Server variables. You could also save output from any of the SQL Server DMV to store various options over time (query plan statistics, wait types, memory, locks etc).

You could investigate using the new Management Data Warehouse feature to collate lots of information http://msdn.microsoft.com/en-us/library/bb677306.aspx.

Having said all of that, that is going to be a steep learning curve and it is difficult to give a definitive answer. As a beginner is buying a third party tool that will do all this monitoring for you an option? Some packages are: -


http://www.sqlsentry.com/products/performance-advisor/sql-server-performance
http://www.red-gate.com/products/dba/sql-monitor/