Alex and Tee,
It probably wouldn't hurt the engine to run it for a bit every couple of weeks. You want to run it long enough so that any moisture in the exhaust will burn off. However, if your rig is like mine, starting the engine with the hydraulic jacks down will get you a constant beeeeeeeeeeeeeeeeep warning that the jacks are down. You might want to raise them first. Assuming your site is mostly level, I wouldn't worry about the slides, but if you want run them in and out too, no harm done.
Depending upon how your chassis & coach electrical systems are wired, you might want to put a small trickle charger on the chassis battery to keep it charged up. But if you start the engine once a week or so, it shouldn't be any problem.
The generator should probably be run every once in a while with a moderate load on it. Obviously, only during the times considered as "generator hours" by the campground. I usually try to run mine once a month for a 1/2 hour, but I'll admit to letting that slip to 2 or even three months, especially during the winter if we don't get a "warm spell". So far, no harm done after 17 seasons.
All that said, other than keeping the batteries topped off, I'd probably say if you left it alone you'd be fine too. Probably the most important part of exercising the systems is to help you stay familiar with everything. Being a new rig and all, you'll probably have a lot to learn.
As for propane, there might be a truck which comes by to deliver, or you might have to move the rig to the propane filling station at the campground. Or, perhaps, to a local filling station. I'm sure a quick call to the intended campground will tell you the details. :)
Another thing I recommend is to make your tires are aired up to the proper pressure before travelling. If you have a tire pressure monitoring system, so much the better. If you don't, then you might want to consider investing in one. I think improper tire maintenance (operating at proper pressures) is one of the most common mistakes RV owners make. So make sure you have the proper pressure gauge(s) and equipment to keep your tires at the proper pressure. Remember that tire pressure changes with temperature. A properly inflated tire at 90 degrees in the summer may be under-inflated at 40 degrees. So the pressure in your tires might be fine when you arrive at your destination, but, 6 months later, depending upon the seasons, it might need to be adjusted to stay within the tire manufacturer's specs. On the other hand arriving in Fall and leaving in Spring might not matter. Arriving in the summer and leaving in the winter could be a completely different story.
Safe travels!
~Rick