Windows Hotmail by default displays Windows Live Home page when you sign in to Hotmail. You can change this behaviour and display hotmail inbox when you sign in to Hotmail. This can be done by using the Hotmail Options.
Click the Options drop down available on the right hand side of Hotmail. Select More options from the menu list.
Navigate to Customize Your mail section and click the Windows Live Home settings link.
In Sign in to Hotmail section, mark the check box with label as Show me my inbox when I sign in. This would take you to your inbox when you sign in to your hotmail account.