All good responses so far. I’ll try to add to that.
First nothing special you need to do with the fuel for storing the vehicle for Id say, a year or less. As said, diesel is much more forgiving than gasoline. If storing long term I’d consider adding a biocide as a preventative measure.
No other additives needed or even preferred (ulsd lubricity or lack thereof is a non issue in newer engines). Except if you’re running fuel in cold weather that has not been treated to prevent gelling.
But even this is not an issue unless running summer fuel in below freezing temps, or changing geographical location from somewhere that doesn’t treat for winter and driving into cold weather. (Example fueling up in Vegas in the winter and then driving N into Utah). But anywhere it gets cold, the fuel is already treated before it goes in the storage tank. In those cases, unless it gets much colder than the average lows for the area, also no concern. (I’ve only seen this happen once, large scale. Denver dropped to -30F one morning and all the local fuel was not treated for that extreme. Most local diesels gelled up for a couple days)
Storage, I always leave tanks as empty as possible. Gas or diesel. With gas, any minor condensation that may happen in the tank gets adsorbed with a good ole fashioned fillip of E10 gas. But suit yourself here. The jury is out on this one.
DEF. Do a little research but bottom line, it’s best to store vehicle LOW on DEF. So you can add fresh when you drive it. You can research shelf life and what affects that negatively (heat mostly). But if it’s cold out the def will freeze and not degrade further. It freezes at 12degF I think. Best bet is do what you can to keep any def in the tank less than a year old.
Or minimize the old stuff. Not too difficult under normal circumstances. Once you get a feel for how much it uses, you can plan to run it low before layup.
Another myth is what def is better for your vehicle. This is purely a myth. Unless it’s old or boxed def was opened, the quality of box def or pump def is both just fine.
Congratulations on the new rig. It’s not too bad “dealing” with diesel. Less concerns than gasoline imo. Just keep your eye on maintaining the quality/age of the def.