I came across the same problem this morning, and after some googling found an answer. It comes down to finding the right tpl.php file and copying it to your own theme.
If you're subtheming from a base theme (in my case, for example, adaptivetheme), the base theme may provide its own layouts. Template files will be included there. The base theme may also implement a
template_preprocess function that you can use to add classes, if that's supported within the .tpl.php.
Panels ships with some built-in layouts. I think that the template files located in the panels module directory under plugins/layouts/<layout>/panels_<layout>.tpl.php will be what your're looking for. I haven't used them specifically, but they appear to follow the same pattern.
If you want to provide a different layout depending on node content type, however, you'd probably want to explore using panels page variants in the node_view panels page. You can change layout and add pane-specific classes there through the UI.