Payment and shipping are handled by extension modules, so you probably installed the Flat Rate module under Admin -> Extensions -> Shipping , selecting the default_flat_rate shipping module.
There are options for cost, location (which regions the module should be used for, I presume) and sort order (change order in which the module is presented on the shipping page.).
There is not an option for a postage or handling fee, within the module itself - but there is a Handling Fee module in the Order Total collection. Try there.
There is no reason you can't offer both Per Item and Flat rate options for shipping - just activate both modules. Not sure the options will always make sense though....
David