On the inventory page on the website, sorting by rarity (highest first) gives the order of Uncommon, Titanium, Rare, Mythic, Legendary, Epic, Common.
I'm not sure of the intended rarity ranking, but I doubt that uncommon should be considered the rarest.
In addition, when sorting via rarity, it does not order any specific way. If you order via rarity, you will get a completely different order within each rarity than you got last time. For example, my next roll had the queue cutter disc first, not a dispenser theme.