I am new to the GECK for one thing so it may be the easiest thing in the world to do, but I don't know how. When I say ownership I don't mean go into edit the container and change it to be owned be PlayerFaction (unless this is in fact how one does what I want to do). I mean when you put items in the container they stay their; I am creating a base and that is essential. I want containers to behave like they do in the Novac motel room or in the suite in Lucky 38. You could just copy the containers from the places I mentioned, but their has to be another way.

It is very easy but only after you know how Edit the container base object and do the following:

1. Uncheck "Respawns" so the container will never reset. (You will find the vast majority of containers in New Vegas do not respawn.)
2. Check "Quest Item" to ensure that NPCs will never loot items from the container.

It's generally recommended to pick an existing container that looks cool to you, then make a copy of the base object by giving it a new ID, that way your container is only used by your mod, and any changes to it (including initial items, if any) won't affect any existing references that use the original base object.

If you want to observe first hand why "Quest Item" is important, fill the dumpster beside the Goodsprings Mojave Express box with cool weapons and ammo before Ghost Town Gunfight / Run Goodsprings Run and then check it again after the fight. Chances are at least one good weapon will get looted during the fight. (That's also a cool way to give the townies some extra firepower if you feel rich enough.)

Also, be aware that even if your container is in an interior cell, unless you setup your cell correctly it is possible for NPCs to go into it and possibly loot containers. It's just a good habit to lock down everything (including the cell itself) that you don't want NPCs getting into. IIRC the cell interior data values of interest are "Owner"=Player and "Public Area"=Unchecked, but I might be wrong on that it's been quite awhile.

Thanks for responding so quickly! I have done what you said and also I was wondering if it is necessary to make the owner of the container the "Player".

Yes that is a good catch. Objects by default (i.e. ownership = none) inherit the ownership of their cell. Setting the container to player owned ensures no matter where you put the container it will be owned by the player, you could even put it inside a cell owned by an NPC.