Hold all these unusual gems in the inventory

Places you can safely store your items include any houses you buy, your companion(s), and your horse.

Places considered to be owned by you (and therefore contain safe containers) are (spoiler warning):

• Arch-Mage Quarters (after you become Arch-Mage)
• The Dawnstar Dark Brotherhood Sanctuary (After you've finished the Dark Brotherhood quest line)

I have personally stored items in my apprentice quarters in the College of Winterhold without problems, however others have had stuff go missing from there, so be careful.

Other containers may not be safe. Given what some other answers have said, Gerder's house does not seem like a safe place for long-term storage.

Certain characters are more shrewd than others and can figure out if they've been stolen from and who did it. One of my favourite examples is Anise (the lady with the shack near Riverwood). She's sent guards to all 3 of my characters.

There's no penalty later on if you decide to talk to them, they'll act like it never happened (I think, or maybe they'll dislike you more, but it's basically the same).

I've also only ever had one set of thugs from each person, even if I continue to steal from them.