Fully display only most recent post on front page, furl the others
You can render a views block within another views page. E.g. you want to show 10 nodes in total, and 1 of them in full mode:


Duplicate the existing view display as a new display of type "block". (Do not duplicate the entire view, only the sub-display by using "Duplicate as block").
In the original page display, in the Pager section, limit the number of items to 1.
In the original page display, in the Format section, set the view mode to full.
In the new block display, in the Pager section, limit the number of nodes to 9 and set the offset to 1.
In the new block display, in the Formatw section, set the view mode to Teaser. While changing the Format make sure to change the settings only "for: this block (override)" and not "for: All displays".
In the orignal page display, in the Footer section, add a "View area" and place the newly created block display. Here also change those settings only "for: this page (override)".