The shopkeepers in river wood and white reach and the trade caravan of kajit aren't buying them. I am nearly maxed out with carrying capacity as is Lydia, so I really want to sell this stuff. Thanks.

You can't use fences until you get the appropriate perks in Speech/you've joined the Thieves' Guild.

Buy a house and store your ill gotten gains in there until you join the guild?

Bummer. Yeah, when I have the coin. What about that ruined house just outside whiter each....there is a chest there.

Anyone know if NPCs ever loot it?

I'm not sure which one you mean, but here's a link to a list of the houses, shack's and other places that you can store things safely http://www.uesp.net/wiki/Skyrim:Houses#City_Houses

Thanks. It is the one without a roof, outside white run just past the watchtower where you fight your first dragon.

Don't take this for sure,but I have heard that, that is safe storage.

I haven't checked yet,but you could store an item in the chest,such as an iron arrow,and come back to it about 14 days later to see if everything is still there.That means the iron arrow and everything.

I'm not even sure about the time,it could be 14 days or it could be 30 days.
I haven't learned any sure answer yet.

I put stuff in the two barrels outside Warmaidens blacksmith until I get Breezehome.

I know it's not safe. But in early game, I'm never gone from Whiterun more than a few days.

There's a barrel in Dragonsreach (to the left through the kitchen and downstairs) that will clear "Stolen" tags. It's the one with the bowl on it. Put the items in and have a follower remove them for you.

About the house, if you can handle 3 thugs coming after you then http://www.uesp.net/wiki/Skyrim:Anise is a perfect choice. It got an Alchemy Lab, an Arcane Enchanter, a bed, safe storages (in basemant) and you can fast travel there.