As for storage I use the robot's house in Goodsprings since I can sleep there as well. He leaves eventually and it's an open residence that I use until I get to Novac. The containers in the hotel room in Novac are all safe too. I've put items in various storage containers in that room and never had any of it go missing.\
Also, as a test, I dropped some items on the ground by the work table in the Crimson Caravan compound and left it there for many days in game and nothing went missing. Can't say that's 100% safe and I wouldn't drop anything unique like that but junk should be fine.
That said I put some things in an NCR storage locker at a tent outside the town of Searchlight and when I came back later my stuff was gone. So be careful and don't put it just anywhere.
As far as junk goes I'm on a personal mission to clean up every single area I visit. So far I've sold off literally hundreds of old books, empty bottles, cans, crap food, tools, glasses, plates, and everything else I could pick up. Netted a few thousand caps in the process and everything looks so much cleaner.
I couldn't stop laughing when I read this post in a different forum.