On the inventory page on the website, sorting by rarity (highest first) gives the order of Uncommon, Titanium, Rare, Mythic, Legendary, Epic, Common.
https://imgur.com/a/9YBumjE
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.