Here's a demonstration of a pretty easy to implement option in the Classic Designer.  This was tested on Version 11.0.2307.40547.

Add a table to your form with CSS Class of sortableTable.  Include a single line field in the table with CSS Class of sortableTableField.  Make sure the field is not readonly and you probably don't want a default value either.  Set the table to "Append rows to the rows populated by a data source or variable" with a range of 0 to 0 additional rows allowed.

Set-up a lookup rule to populate some list of values into the field in the table.  It doesn't need any conditions, but you probably want a relatively short list.  Be sure to check the box for loading them "as new rows".

Add this CSS to the form: 

.sortableULField {
    margin-top: 10px;
    margin-bottom: 10px;
    margin-left: 20%;
    margin-right: 20%;
    padding: 5px;
    border: solid;
    text-align: center;
    font-size: large;
}

Add this Javascript to your form: 

$(document).ready(function() {
  
  //Hide the table with the sortableTable class, it's just used to save
  //the values, and will be updated using another component.
  $('.sortableTable').hide();
  
  //Create the list of sortable elements when the form is loaded, when 
  //lookups are complete, and when changes to the sortableTable table happen.
  //Then manage the sortable element and update the table when the sortable
  //elements are dragged.
  createSortableElements();
  $('.sortableTable').change(createSortableElements);
  function createSortableElements() {
    $('#sortableULStructure').remove();
    var htmlStructure = '<ul id="sortableULStructure">';
    $('.sortableTableField input[type="text"]').each(function() {
      htmlStructure = htmlStructure + '<li class="sortableULField">' + $(this).val() + '</li>';
    });
    htmlStructure = htmlStructure + '</ul>';
    $('.sortableTable').after(htmlStructure);
    $('#sortableULStructure').sortable();
    $('#sortableULStructure').on( 'sortupdate', function() {
      var childCounter = 0;
      $('.sortableULField').each(function() {
        $('.sortableTableField input[type="text"]:eq(' + childCounter + ')').val($(this).text());	
        childCounter++;
      });
    });
  }
  
});

//When lookups are complete, trigger a change which will trigger
//other changes with the other code.
$(document).on('lookupcomplete', function() {
  $('.sortableTable').trigger('change');
});

The end result will be a list of values in a format that can be dragged around in priority order, and the values will be saved in the fields.

However, be aware that the code isn't optomized for read-only version of the form, so if displayed read-only or archived to the repository, it won't display as expected.  For read-only or archival, you should have an alternate version of the form without the Javascript, and with the actual table formatted how you'd like.