Following the main quest a bit further, I stumbled upon an opportunity to buy a house in Whiterun. You have to complete the Dragonstone quest (Bleak Falls Barrow), then you'll be granted the right to buy a house in the city.
To buy the house you have to speak to Proventus Avenicci, he's near the Jarl in the keep. Unfortunately the house is pretty expensive for a starting character, it costs 5000 gold.
The house itself is called Breezehome, it is the second house on the right when you enter Whiterun.
Within a couple of days, there is no respawn. Respawn now takes 30 ingame days, which is longer than in previous ES games.
You even get a "cleared" marker on the map when you eradicated an area of all its inhabitants for the duration.
However, when you have not fully cleared sites, enemies may respawn. I experienced this myself at some fort which name I can't remember right now. I killed 3 of the guys outside, went into a tower inside the fort, came out again and they respawned.
By the way, storing stuff inside containers which do not explicitly belong to you (e.g. stand in your house) doesn't seem to be safe. At least one of the loading screens explicitly says that storing anything in "wild" containers does not guarantee for it to be in there when you look for it the next time.
One way to find a dungeon which has respawned enemies inside is to accept one of the various kill quests that you can find (from innkeepers, the Dark Brotherhood, etc.), which will lead you to you to these dungeons. These procedurally generated kill-quests will send you to dungeons where the difficulty inside matches your level, which means that taking one of these at higher levels will have a higher likelyhood of taking you to a more difficult respawn-dungeon.
Best Answer
Ive had my items stored in my spouses house for around two weeks and they are still there, so, yes I believe containers in your spouses house are safe. EDIT: They have been there for several months now without loss. Your spouse's house is safe.