You can easily get menu items in Joomla.
To get the menu:
$menu = JFactory::getApplication()->getMenu();
To get menu items by attribute:
$items = $menu->getItems('menutype', 'mainmenu');
The variable $items is an array of menu item objects. It contains the following:
To get the active menu, and then its parameters:
$current = $menu->getActive();
$params = $current->params;
$yourParameter = $params->get('yourParameter');
To get the default item by language code:
$default = $menu->getDefault();