Adding different containers to different parts of content from a node
The Field Group module will allow you to group fields into containers you may then be able to alter some of the mark up with the Fences module. 

It does sound like you need more control so if those modules don't work you'll have to get your hands dirty in some code. The template files node.tpl.php and field.tpl.php should give you all the control you need over the mark up.