Lots of people have suggested hoses etc. I've been using my Scamp for 4 summers now, and have never used the water tank. It saves on weight (8 lbs/gallon) not to be hauling water around, and you don't have to winterize. I always know my water is truly fresh and clean, and I don't have to wonder what may have grown in the tank or lines since the last time I used it. 

Just a thought, of course. Others' opinions about what's necessary will be different. I just prefer to keep it as simple as possible. 

Wheel chocks are critical safety equipment. For leveling, some people get fancy purpose-made leveling blocks; I just carry a few pieces of 2x4 and 1x8. Bringing a level is a good idea. You could also, at some point, get some of those RV leveling bubbles that you can stick on the outside of the trailer, and thus have one less thing you need to drag around.

"Laundry list": You'll want a lighter of some kind for the stove. Extension cord for shore power (from the house, for instance, and get a GOOD one, not a cheap one). Whisk broom, as mentioned above. I'd use a non-fabric mat outside, something that will dry quickly. A throw rug inside will be a comfort, but not necessary. Carpet samples will work too of course, at least inside, but if they get wet they might take a long time to dry. Minimal cooking/eating gear: true essentials only, until you know what your Scamping style will be. Paper towels, wet wipes, a box of tissues, and soap. I use bar soap because it can't spill or leak. Some kind of basin to wash in. I'm really happy to have a tiny little trash can that I put under the sink. For a long time I just hung a plastic bag on the forward curtain rod, but that was kind of ugly, and it fell down all the time anyway. For convenience, if you're charging devices using the 120v outlet,  maybe you'll want something like this: https://amzn.to/2SAGg71 I'm not recommending this particular model, just the form factor. 

I keep spare device charging cords inside the Scamp, so I don't have to remember to pack them.

Be sure to have tools to handle the easily foreseen emergencies: sockets for wheel nuts (and I brought a super-long-handled torque wrench and extender so as to get enough leverage and clearance to get those nuts off), and a deep well socket for the clamps that hold your LP tank on. A multi-tip type screwdriver. Needlenose pliers, crescent wrench, and utility or other knife (for, among other things, opening those people-proof plastic packages you have to break into when you forgot something and had to stop at a box store to pick one up).

Some people like to bring LOTS of tools, for every conceivable problem. I dunno... For me, the Scamp is at heart a glorified tent. Although I've done a whole bunch of decor changes inside it so that it's now a delight to spend time in it, its true purpose is to be shelter. As long as I can tow it to where I can get help with it, I'll still be all right if the electrics fail, the refrigerator doesn't work, the lights don't come on, and I run out of propane.  

On my first trip I assumed that the seven-pin electric connector and brake controller I hired installed actually worked, and that the car's alternator was handling the Scamp battery and powering the refrigerator. The running/brake lights etc worked. But no. I arrived at my destination only to find that the Scamp's battery had been completely drained by the refrigerator, because the wiring connections on the tow vehicle had not been properly installed. Meh. It was inconvenient but I wasn't too worried. The propane worked fine for the fridge, and I had pinned three sets of AA-battery powered fairy lights to the rat fur of the Scamp ceiling (just angled in some long straight pins so the lightweight wires are held in the angle, battery packs attached in various out-of-sight locations near ceiling using hook-and-loop stickies); it was just a whimsical decorating/ambience idea, but sure came in handy. Those lights were all I needed for the evening. I also had a battery-powered folding 10" fan, which was just enough to cool me off until temps dropped for the night. The next day I took my Scamp battery to a nice little one-man garage in the closest tiny town, and he charged it up for free, over the course of the day. Fetched it back, re-installed, and I was back in business: LED lights and ceiling fan working again, which is about all I use in the summer.  Moral of story: Have some sort of backup light source, at a minimum. I do recommend the fairy light idea though: those things seem to run forever on a single set of batteries. 

Get some of those easy-install/easy-remove utility hooks you can stick up unobtrusively, here and there. You'll want something to hang your wet cleaning cloths or damp towels on, and to loop your umbrella strap over. 

Choose a place where you will *always* keep your car keys, and don't put them down anywhere else. ;) I once "lost" my keys and searched madly for them for 10 scary minutes, before finding them hanging in plain sight on that potholder hook I put up on the backsplash over the sink. 

In the interest of keeping things cleaner inside the Scamp and nice to walk on barefoot outside, I got an RV patio mat, which I really love. 

When you pick up your Scamp, check to make sure things that should be level really are: the hanging rod in the closet, for instance, and the table. I didn't notice right away that my table wasn't installed level, and it's too late now to get warranty work. It bugs me visually, though it works fine. DO plan to spend a little time camping nearby, so you have time to notice and report stuff like this.

Enjoy your new Scamp!