To change the order that your organisation's Book Types appear on the Booking Skin go to the Web Control Panel <YourCountry><OrgID>/Admin> > Web Module Settings > Seats > Book Type Ordering 

You can either select Alphabetical sorting: 

Or Custom sort order 

Beware: these changes are GLOBAL. Change the order of Book Types here and they will be changed on ALL of your events.

As soon as you click Custom all of the Book Types your organisation has used/is using will appear - no matter whether they are used for any particular production or not. 

To select a Book Type click on the row it is in and hold the left mouse button down, while simultaneously dragging it up (or down). The mouse pointer will turn into a 4 pointed star while in this mode

Drag and drop the Book Types up and down to reorder them, then Save Settings (bottom right)