You can order the links in a link party from the +Advanced options while creating or editing the party.
There are four different sorting types:
Oldest: This is the default option. It places the links that submitted first at the bottom of the collection. This way usually the first one to enter gets the most views (clicks).
Newest: With this option the latest links are displayed first. Everyone gets a chance to be on the top entries. Latecomers get their chance to!
Alpha: This option orders links alphabetically. When links are sorted in alphabetical order, enable the "Don't show the index number for each entry" option as well to drop the numbers, as there is no need for numbers when links can, at any point, be inserted in the middle of the list.
Random: When links are sorted randomly, each time the collection is displayed, the links are in a different position. This is a good option when it comes to photo challenges where you should judge by content. No numbers are attached to the thumbnails by default.