List of items to take with you when picking up your trailer.

I would add a "roll of mechanic's wire" to the list.

If find the trailer lights are not working, just back out a couple of the "J" rail screws and wrap a couple of turns of the soft mechanic's wire, then go across the rear and do the same to the other side. The temporary tail lights that you brought can be hung from the wire securely. It sure beats taping the lights to the skin, and is easy to remove when you get it home.

The easy way to bring one home is Soup's truck or my tandem axle flat bed. Then you fix everything after you get it home.

Cheater blocks attached to inside walls under bench lines so they don't show. Try to hit a wall stud. The cheaters have to be wide enough to over lap the floor to hold the walls up. All you need is 4 of them with screws, pre-drill the cheater blocks. Only takes moments to install before that 1st transport. Heck install 8 of them and camp all season before repairs LOL

I keep a supply of tie wraps in various sizes and they come in handy for hanging wires, or dragging chains. Also, duct tape came in handy for loose jalousie panes! Check them before you move it!

That puts the tires around forty years old I wouldn't pull them across the street let alone a three hour trip.
Replace the tires and yes if has brakes they could be rusted solid, You should repack the bearings and replace if needed. next examine springs, attaching hardware, and the frame for defects. also make sure the coupler is free and latching properly with a safety retaining pin and good safety chains.
You also want to make sure the walls aren't rotted around the bottom as this could allow them to fall while towing it home that is addressed above and in several other places.
It will be a miracle if the tail lights work so take along a set of magnetic lights as soup suggests above.
Also make sure all window glass is secure so that it won't fall out going down the road.
Next be sure all doors, including compartment doors are securely fastened to prevent them from flying open.
Not trying to scare you just trying to keep you and your new trailer safe on your trip home.
My final suggestion is tow it at a reduced speed no more than 50 or 55 mph. slower is better until you get it completely checked out. Stay safe and enjoy or new trailer and welcome to the board.