The 5 things you really need are: A water hose, an electric cord, a sewer hose, your tanks full of propane, and tire chalks. The length of each cord or hose is determined by your own comfort level. After this, absolutely everything else is just personal choice.
You "should" have something to level the trailer (blocks under the tires) and blocks for the stabilizer jacks. The kind you use is your choice.
You "should" have a water hose pressure regulator, but nothing says you MUST. You can always fill your fresh water tank and then use the on-board water pump, which will NOT create more pressure than your system is designed for. (so this is really, your option).
You "should" have a Surge Protector (Progressive, or Surge Guard), and you'll get all kinds of recommendations for each one, and why. The cost and the functionality can is endless on these. Do you "really" need one? Actually no, but it is a good insurance again power spikes and low voltage. You really need to consider a Surge Protector as an "insurance". Most of the time, it's never needed, but the one time it protects your camper, it's worth every penny it cost. (still, a personal choice, not essential).
You "should" have a set of breakdown tools. But here again, how mechanical are you? A pair of pliers and a screwdriver, a socket wrench to remove the anode rod in your water heater, a back-up took to raise and lower your stabilizer jacks.
You "should" have extra household extension cords. Some you can plug in at the campground post (like 50 footers) and some you can use inside the camper. Both come in very handy, especially if you use electric appliances outside.
Absolutely every thing is a "you SHOULD" have, and is selected by your own comfort level and personal choices.
Now, outfitting your new camper is pretty much like outfitting a new house. THERE IS NOTHING SPECIAL OR DIFFERENT ABOUT CAMPING EQUIPMENT THAT YOU WOULD NORMALLY USE INSIDE YOUR STICK-AND-BRICK HOME. The only exception might be outdoor folding chairs, or a hot dog stick used over a fire (unless you have a fire place or fire pit at home and you already use hot dog sticks), or a hatchet or a good all purpose hunter's knife.
Whatever you use in the house, you will use the same things when camping. You still need a reliable can opener, a bottle opener, maybe even a wine bottle cork screw. You still need dishes (if that's plastic, pager, or china). Some folks used whatever extras they have laying around the house. In time you will stock your camper with it's own "stuff" that won't migrate back to the house. In time you will replace things inside the camper, and start purchasing new. Over the next couple years, almost everything you put in the camper will be replaced with something different. It just happens. In 3 years, you'll be throwing "stuff" away or giving it to GoodWill.
But here's the things you'll need to "stock" in your camper for a happy camping trip.
It is assumed you have leveling blocks, chocks, water, electric, and access to dump your tanks.
You need to "outfit" your camper with:
Bedding
Personal hygiene items, including bath towels and wash cloths.
Dinner ware
Cook wear (don't forget the can opener, potato peeler, and coffee pot)
Clothing
House cleaning items for floor, bath, and kitchen) (That may be a simple broom to a whole house vacuum system, bleach, laundry soap, etc.
Entertainment (whatever that may be for you: games, books, hobbies, hiking, or just vegetating)
Outside the camper:
You may want to keep stocked cleaning supplies, for washing windows, or removing bugs from the front cap, tire cleaners, and waxes and polishes.
You may want your own style of lawn furniture. A tree log works OK for a chair, but a zero gravity lawn chair is going to be much more comfortable. It's all your choice. But you want something to sit on outside.
You may want table cloths for the campground supplied picknic table.
You may want your own outside table, a dishwashing work station, an outside BBQ grill, a stand along pop-up shade (like Quick Shade).
You might want a television to set up just outside. You might want to bring along an outside electric cooler so you don't have go to inside every time you want a drink.
You might want to bring along a fire place poker set for camp fires, hot dog sticks, Cast Iron, Dutch Oven cook ware or an electric skillet. It's really whatever you want. You can even wrap potatoes in aluminum foil and toss them in the fire, or simply put your can of pork-and-beens right on the fire coals and use the can as your cooking pot!
Simple, or complex, it's really all up to you. No magic formula. It's just whatever you want and what fits your life style.
The 5 "absolutes" are listed above, after that, really .... everything else is just personal comfort.