So up until now, I have been storing my stuff in my room at the mages guild. I am planning to move my stuff to my new house. I heard that some containers like barrels are unsafe because they will reset and delete all the items in them eventually. I wanted to know if that was true. Remember these are the containers in a Homestead.

Containers in a house should all be safe, although a couple of barrels in the house with Lydia can reset (UOP takes care of this). However I have never lost anything in a house, including the house with Lydia or that I owned or built.

Furniture never respawns, anywhere. A couple of chest types are set to respawn, mostly boss chests in dungeons and a couple in places like the common houses.

http://www.uesp.net/wiki/Skyrim:Containers#Safe_Containers

http://www.uesp.net/wiki/Skyrim:Containers

The biggest issue is storing things in an owned container, that will transfer ownership and you will be stealing when you take it back out.