PHP - Number Frequency

I have several forms which will request the user to select one of several options where the most common choices will be pronounced, and might look something like:

The client is responsible to determine which ones to display (opposed to hiding within "more choices") and the server is responsible to provide the list of options along with some means to determine which ones are most common.

For a new user, the order will be based on my "best guess", however, whenever a user selects a given option its ranking for that user only should go up, and in addition more recent activities should have more bearing on the returned order.  In addition, there will be more than one of these lists and each of these lists will expose a public identifier (most will use a string but some might use an incrementing integer series) instead of the primary key.

I have some fragmented ideas how to best implement but would like other people's thoughts on how to best do so.

Starting with the list schema, undecided on which approach below.  Any preferences or something else altogether?

Solution 1:

abstract_list
- id (INT PK)
- discriminator (string)
- name (string unique with discriminator)
- ranking (TBD whether float or integer. This represents my initial "best guess")

list1 (list2, etc)
- id (FK to abstract_list.id)
- discriminator (FK to abstract_list.discriminator)
- public_id (string or integer based on specific list. unique with discriminator)

Solution 2:

abstract_list
- id (INT PK)
- discriminator (string)
- name (string unique with discriminator)
- ranking (TBD whether float or integer. This represents my initial "best guess")
- public_id (Application responsible to cast as string or integer. unique with discriminator)

list1 (list2, etc.  This class has no properties and only a method to cast the public ID as required.  Seems like a waste...)
- id (FK to abstract_list.id)

I will then add another table to join each list to the user.

user_list_ranking
- abstract_list_id
- user_id
- ranking (TBD)

To retrieve the list options, will query abstract_list and LEFT JOIN user_list_ranking and then sort on some mathematical formula acting on abstract_list.ranking and COALESCE(user_list_ranking.ranking, 0).

To promote recent activity, maybe increment user_list_ranking.ranking every time the user selects a given option and also decrement all other options of the associated list.  To prevent excessive windup, cap the the value to some max value (i.e. If list1 has a total of 10 records, cap it three times that value resulting in 30), and cap the minimum at zero.  Uncharted territory here and am very open to other approaches.

I am undecided whether I should just return an ordered array of the options, or also include either an order integer or some normalized value from 0 to 1.

If there is a common way to do this, please let me know what it is so I may mimic it.  If not, please provide any critique or recommended changes to my intended approach.

Thanks

|  id          | int(4)       | NO   | PRI | NULL    | auto_increment |
| user_id     | int(4)       | NO   |     | NULL    |                |
| recipient   | varchar(30)  | NO   |     | NULL    |                |
| subject     | varchar(25)  | YES  |     | NULL    |                |
| cc_email    | varchar(30)  | YES  |     | NULL    |                |
| reply       | varchar(20)  | YES  |     | NULL    |                |
| location    | varchar(50)  | YES  |     | NULL    |                |
| stationery  | varchar(40)  | YES  |     | NULL    |                |
| ink_color   | varchar(12)  | YES  |     | NULL    |                |
| fontchosen  | varchar(30)  | YES  |     | NULL    |                |
| message     | varchar(500) | NO   |     | NULL    |                |
| attachment  | varchar(40)  | YES  |     | NULL    |                |
| messageDate | datetime     | YES  |     | NULL    |        

            $params = array(                 
               ':user_id' => $userid,                 
               ':recipient' => $this->message_vars['recipient'],                 
               ':subject' => $this->message_vars['subject'],                 
               ':cc_email' => $this->message_vars['cc_email'],                 
               ':reply' => $this->message_vars['reply'],                 
               ':location' => $this->message_vars['location'],                 
               ':stationery' => $this->message_vars['stationery'],                 
               ':ink_color' => $this->message_vars['ink_color'],                 
               ':fontchosen' => $this->message_vars['fontchosen'],                 
               ':message' => $messageInput,                 
               ':attachment' => $this->message_vars['attachment'],                 
               ':messageDate' => $date             );

$sql = "INSERT INTO messages (user_id,recipient, subject, cc_email, reply, location,stationery, ink_color, fontchosen, message,attachment) VALUES( $userid, :recipient, :subject, :cc_email, :reply, :location, :stationery, :ink_color, :fontchosen, $messageInput, :attachment, $date);";

And lastly, here is how I am calling it:
            $dbh = parent::$dbh;             
           $dbh->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_WARNING);              
           if (empty($dbh))    return false;             
                  $stmt = $dbh->prepare($sql);             
                 $stmt->execute($params) or die(print_r($stmt->errorInfo(), true));              
           if (!$stmt) {    print_r($dbh->errorInfo());              }

public function Update(Entry $e)
    {
        try
        {
            $query = "update entry set string = $e->string,delimiter=$e->delimiter where entryid= $e->id";
            $stmt = $this->db->mysqli->prepare($query);
            $stmt->bind_param('ssi',$e->string,$e->delimiter,$e->id);

            $stmt->close();
           

        }
        catch(Exception $ex)
        {
            print 'Error: ' .$ex->getMessage();
        }
    }