The game chooses a random item from a subset of 62 items (10 rings, 37 goods, 9 weapons, and 5 armor pieces) to display on the loading screen. By default, these items are generally consumables or online items you find relatively early in the game, equipment belonging to assorted NPCs such as Siegmeyer, Oswald, and Logan, and some other extras like the Skull Lantern and Red Tearstone Ring.
The IDs of these 62 items are hard-coded as 248 (62*4) bytes in the executable, starting at offset 0xEE4FA0 in Prepare to Die Edition, or 0x1ACC9B0 in Dark Souls Remastered. In Dark Souls Remastered, they are loaded into memory at [exe]+0x141ACE7B0, if you'd like to edit them while the game is running.
The first three bytes in each four-byte set specify the item ID, and the fourth byte specifies the item type (0x0 for weapon, 0x10 for armor, 0x20 for ring, and 0x40 for good).