This game is awesome! Where is a "for sure" container I can dump my stuff? I've been to Riverwood and Whiterun only. I don't have money yet just need a container.

I believe there is a chest right next to Ysolda's house. I think it's safe for storage. You should probably check UESP for more details. Also, I think Anise's Cabin is safe. Again, you could check UESP to be sure.

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

Here is a list of houses, some you get from the game, some, you just take over

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

This one. The chest is safe.

It's a really small one next to some barrels on the side of her house.

Across the river from Riverwood is a cabin.
In the basemant of this cabin is a chest,that is safe storage close to where you are now.

Of course