When using event archive page which has default slug http://www.your-domain-name.com/tc-events, events are displayed in order of their creation which is visible in the table of the existing events in Tickera -> Events area. Yes, we agree that most of the time that is not the order you need so, to change the order on the front end, you will need to reorder events in that table. The most efficient way to achieve this is by utilizing this free plugin which will allow you to re-order events just by dragging and dropping events in that table and that will reflect the order of the events on the front page as well.
Same principle can be applied for the ticket types when using a shortcode for displaying the table of all the available tickets for certain event or when using Show Tickets Automatically option on the event page.