Why did some of my items disappear from a barrel?
This is because you stored the items in a container that isn't safe.
WARNING: Don't put items on a container you don't own. They might not be there later.
It seems that that except for the potatoes, quest items won't be removed from the container.
Where do I store all of my stuff?
There are different containers of storage. Here are ways of some.
Own a house where in any container, you can store stuff without resetting. You must become Thane of a hold to buy a house. You can also store items in Anises Cabin after you kill Anise, but don't store items in the barrel. Bets in the basement. You can also store items in your spouses after marriage.
Companions. Ask them to trade and give them the items you want to "store". They will still have it. An easiest way to get one is to complete a Love Triange quest starting in Riverwood by talking to Sven or Faendal. Whoever you trust becomes your follower.
Some random containers are safe storage, such as:
The drawers in Helgen. After completing Unbound you can go revisit Helgen and there are some bandits to kill. Inside the inn if a drawer for safe storage.
In the Riverwood Inn the chest in the Blades room is safe. You must help Delphine in the main questline first [not all the quests, which mean you don't need to kill that Paathurnaax!].
What about storing things in the Guilds' Hall?
I found out that the bedroom you get when you join the College in Winterhold is not safe! Instead, complete the questline to become Arch Mage allowing you to have your own quarters where storage of items are allowed.
In the Thieves' Guild the only containers that aren't safe are the Tribute Chest and the locked containers in the training room. Instead, store them in the drawers or in the other chests.
The containers in the Companion's mead hall is not safe either! Even if you complete the questline and become Harbinger, there's no safe storage!
Source that these reset.
So that's why your items disappear. You need a container that don't reset! And I showed you some! So that's my answer to the question! Good dragon hunting and gaming!