How To Store Materials For Additional Job Site? Enclosed Trailer? Other?

I'd say a Jobox, security cabinet, etc would satisfy your needs and would be cheaper & more secure than a trailer that can be driven off with. 

My go-to is just to chain ladders and larger devices to the box itself when we were done for the day, as all it did was make walking away with it look like it was going to be even harder. 

They even have "Field Office" styles that give you a little bit of drafting / laptop space.

I guess it depends on how cheap you can get a box trailer for, the most expensive field office box is ~$4k. Normal boxes range from the hundreds to max ~$3k.

A trailer seems like overkill, unless you're going to have a lot of cable spools. Just get a job box and a heavy bicycle chain with a good lock. Put all your stuff in the job box and chain your ladders to the outside. A job box can be transported inside your vehicle instead of having to be towed. 

Install an alarm panel capable of cellular communication inside the job box. Connect a magnetic contact and a seismic sensor inside the job box, so you can get alerted if anybody tries to open it or remove it. The keypad can go inside the job box, but make sure to shorten the delay time to 30 seconds or so. If you really want to get fancy, connect an IP camera to the alarm panel so you get a snapshot of the person opening the job box. This video on putting alarm panels inside networking racks shows the basic concept. 

If you do get a trailer, make sure everybody is comfortable driving and parking with it. Mandate that all your employees take the trailer out into a big, empty parking lot so they can practice driving, turning, and parking. 

We will have quite a bit of material. Several boxes of cable, 5 or 6 14'poles,ladders, 400'~ of PVC, possibly a trencher(probably only for a couple days) shovels, environmental enclosures, bins for all the various PVC fittings, etc.

I can get a 20' storage container for $90 a month, and $150 delivery/pick up each way. I can pay to have it moved to a different job site as well.

An enclosed trailer is around $2,000 for a 6x12 which may be a tad narrow.

I really like the storage container but it is tougher to move around the site.

A storage container seems like a no-brainer to me. While I don't know about the costs for these Construction PODS, they seem like they have a well defined market that you seem to fit in.