Save the players data using Datastore service. There are modules that make it very easy to implement a secure and reliable datastore system (such as Datastore2 and ProfileService). I recommend ProfileService as it has session locking.
As for how you would save the order. Just have a dictionary of the players currently equipped items and their designated slot.
E.g:
local MyEquippedItems = { Slot1 = "Banana"; Slot2 = "Sword"; Slot3 = "Gun"; -- etc }; When the player joins → access the datastore and load the players weapons into the correct slots