I'm new to this site but I'm now on TT #4 as well as experienced with trailers (5000 gal tank trucks in particular) while in the Army.
It may sound preachy, but focus #1 must be safety. Understand exactly what you are doing and if something doesn't seem quite right...it probably isn't! Especially if you have a used rig, make sure your tires are sound and the lug nuts at the proper torque. TTs aren't really that dangerous unless someone is doing something stupid...then they can be deadly and bad things happen fast.
Second point that I don't think many think about until they've been ripped off once is security. Change all the compartment locks. EVERYONE has keys to CH751 locks! Put a lock on your receiver pin or you WILL lose your expensive hitch someday (don't ask me how I know that!). Then while on the road, lock the hitch latch to keep someone from stealing the rig while you're enjoying a nice dinner somewhere. Then get a hitch lock to prevent someone from stealing the rig while it's parked. And finally, I'd recommend a set of lug nut locks, especially if you have nice aluminum rims like on my newest rig. A little tougher to secure is the batteries and LP cylinders. So far no one has stolen those, but I think finding a way to lock them as well would be worth the effort.
Sorry to sound gloomy or paranoid, but I've been ripped off a couple of times in ingenious ways and also had someone smash a window and break in that way while the TT was in storage.
I sleep better and have much less stress knowing that I've at least hardened my security a bit hoping that thieves will go after someone else.