How can I use different template for the Home page, and different template in the inner pages ?
In Joomla! you can assign templates to menu choices.
Joomla! 1.5
In Joomla! 1.5.x you do it in the template. i.e. Select Extensions->Templates then click on the template you want to assign to a menu position. Once in the Template [Edit] screen you can use the "Menu Assignment" panel on the bottom left to specify which menus use the template.
Joomla! 2.5
In Joomla! 2.5 you can set where the template is used in both the Template (similar to J1.5) and you can select it directly in the menu when you're creating it.
Don't forget that in Joomla! 2.5 a template can have "style" variations that you can create and use just like a the base the template.