You may want to do all 5 tutorials if you haven't done them yet as they'll contain the tools you need to achieve this.

First you create your page type for your custom page, on this page type you set up a has_one relationship to a 'folder' and add a TreeDropdownField to allow you to select the folder in the CMS.

class MyPageType extends Page {

public static $has_one = array(
'ImagesFolder' => 'Folder'
);

public function getCMSFields() {
$fields = parent::getCMSFields();
$fields->addFieldToTable('Root.Content.Main', new TreeDropdownField('ImagesFolderID'));
}
}

Then after running dev/build you can select the folder in the CMS backend. To select the images from that folder you can add another function to that class

function getUploadedImages() {
return ($this->ImagesFolderID) ? DataObject::get('Image', "ParentID = '$this->ImagesFolderID'") : false;
}

Then use <% control UploadedImages %>... <% end_control %> to loop the images.

* Note you may run into syntax errors