The box you are going to buy is able to be wired for 240v operation. In a 240v application, you would have a black wire, red wire, white wire (neutral), and ground.
The black wire and red wires are both called the hot legs (black leg and red leg), and the voltage between them is 240v. The voltage from either the black leg or red leg to the neutral is 120v.
When you install a two pole breaker in the breaker panel, it will clip onto both the black leg and the red leg. A two pole breaker is for 240v high power appliance, like a stove. In order for this to work, the black leg buss bar and the red leg buss bar need to be next to each other so that a double pole breaker can plug into both busses. That's why the buss bars are arranged like they are.
But in your trailer, you only have one "leg" which is the black wire in your power cord that plugs into the pedestal at the campground. You don't have a red leg. So there is nothing to attach to the red lug in your panel. That means that only half of the breaker slots would have power, the ones that are connected to the buss bar that holds the 30a main breaker.
So buy a 30a single pole breaker, attach the black wire from the power cord to the screw terminal on the breaker, and plug it into whatever slot you like. Power will flow in through the power cord, through the 30a breaker, and into whichever buss bar that breaker is plugged in to.
You'll also need to buy all new breakers for the new box. The old ones won't work as they use a different clamping method to the buss bar.
In order to get power from the buss that holds the main breaker over to the other buss bar, you need to add a jumper wire (#10 wire) from the black leg to the red leg. Otherwise you will only have power to half of the breakers in your new panel.
The two lugs that need to be connected are the ones that are at the ends of the buss bars. In your picture, one of the lugs is mostly hidden behind the neutral bar. The other is to the right and below the main lug for the neutral bar. You might be able to use the red wire from your original box, but it may be too short.
Sorry it took me so long to get back to you. Good luck, post again if you have questions. It sounds like you are well on your way.