What padlock

It does not matter.

I just kept a cartoon sized brass hardened lock. Anyone wanting into that trailer would just saw through one of the walls. A little 4 x 4 foot chop will get them through and in nicely.

 

If you're the one paying; get cheap bicycle padlocks with the long shank.

 

Then, get the ones on the right in the picture you posted; Master Lock with long shank.

 

Don't buy anything you can't cut off yourself. Mechanism will inevitably rust unless you take good care of it.

 

I consider the lock as more of a deterrent. One that discourages the brilliant mind of BillyBob from thinking about it.
You don't think Stop in security. You think slow down. If you slow them down enough. It does it's job. They either quit. Or they get caught.
I have something like this. Versions of this available everywhere. I got mine at a hardware store.
https://www.amazon.com/Master-Lock-...nology/dp/B07D8414DT?ref_=fsclp_pl_dp_12&th=1

 

I just put lock on when they require them as soon as I pull away take them off. Especially in winter then if I have to park put it back on

 

We get issued a sturdy Master lock for our use and they want us to use it every trip.

With one of our loads in Memphis and one in Atlanta, they just cut the hasp on the door with a grinder in the middle of the night... bypassed the lock completely..... the drivers were sleeping in the cab.