Taxonomy menu limited to certain number of terms
I believe the easiest way to do this is to create a view that block displays a set number of items in a list (HTML or unformatted list), with a global text field that will link to your term page. You can then style this with css to look like the rest of your menus (if you require to).

This unfortunately will mean that it will not go through the drupal core menu system. You will have to create your own "Admin" view to manage this "menu". I would suggest Draggable Views if you require a webmaster to control the sort order.