Creating new content/node
Provided you have a rule that triggers when a user joins a group, and a condition that checks that the group is the group you want, then add a execute PHP action to that rule that runs this code :

// Build a new node object
$node = new StdClass(); 
// set the type
$node-&gt;type = 'your_content_type';
// set the language
$node-&gt;language = LANGUAGE_NONE; // or whatever language you use.
// this fills the node with the default data
node_object_prepare($node);
// set a custom title
$node-&gt;title = 'Nice title';
// set whatever you want, for example body
$node-&gt;body[LANGUAGE_NONE][0]['value'] = 'This is some text for the body';
// Set the formatting for the text
$node-&gt;body[LANGUAGE_NONE][0]['format'] = 'filtered_html';
// Save the node to the DB
node_save($node);
// If you need the node ID
$nid = $node-&gt;nid;
// Just for debugging
watchdog('your_module','Just inserted the node with nid = '.$nid);


The key here is that node_object_prepare sets some default values for your content type.