separating home page and posts

assuming you are working with Twenty Eleven:

start by crating a child theme to make your edits with: http://codex.wordpress.org/Child_Themes
do not edit Twenty Eleven directly – it is needed in case of problems with your site; and you will loose all customisations when you update the theme.

if you are using the ‘showcase’ template for the front page – this has the ‘recent posts’ section;
to remove this, see: http://wordpress.org/support/topic/removing-recent-posts-from-showcase-template-in-twenty-eleven-theme?replies=6 or use the forum search to find other solutions.

to have sidebars on more than the index pages, possibly try to use a plugin http://wordpress.org/extend/plugins/twenty-eleven-theme-extensions/