So my inventory is quite full and I have nowhere to store it.. What are my options?

Plenty. Pick a location in the wasteland that has at least one container, and make sure you didn't kill any respawning NPCs near the building when you first discovered it. Go inside, find a container and put a single item inside it. Leave, go back outside, fast travel to a far away location and wait for 3 days. After that, fast travel back to the building you chose and see if the item is still in the container. If it is, then that means the container doesn't respawn and is safe to use. Containers don't have weight limits so you can store all of your stuff in a single container. Try not to use Metal Boxes though as iirc they do respawn occasionally, but I'm not 100% sure on that.

And that's it. Almost any container in the wasteland is suitable, so long as it's not near any NPCs that might steal your stuff. Personally, I use the desk in the Highway Patrol Building on the road a little south of Primm.

How much can the delivery service containers hold? Bonus being that they can be accessed from many places

They can? That sounds quite awesome to be honest. I hope those containers are meant as storage then.

Somebody confirm this. I am away from home atm

I just checked it out... it kinda works, but isn't ideal. You can put in a lot of stuff, but you ship it from one location to another, and can choose to receive that shipment when you go to the other location... but it could work with some stuff, just very awkward.

Here's a location:
This appears to be an ideal location - some storage, workbenches, and there didn't appear to be any critters or NPCs in the immediate vicinity. It's also got a map anchorpoint, so you can fast-travel to it.

I'm gonna use that thanks

I'm using an ammo container in Victors Shack for a test. Not a close fast travel point, which is in front of the Goodspring saloon, but it currently has robot protection. :fallout:

is it safe to use a container in the gas station in good springs?

Can low level chars get there without being eaten by radscorps??

There's a place where you can rent a room...it's one of the first places one goes to I think, but I'll spoiler it just in case.