OK, I am also going thru this process with my new trailer, but I think I pretty much have the essentials...
-20' sewer hose (kit comes with 2 10' sections, caps, etc) with a clear section to see what is coming out.
-disposable gloves
-2 10' white potable water hoses (for drinking water only)
-1 25' regular hose for rinsing sewer hose, etc. (not for drinking water!)
-small tool kit from Walmart, plus a square ended screw driver
-brass elbow attachment for water hose
-water pressure regulator
-30 amp electrical cord and adaptor
-set of leveling blocks (plastic set,much lighter than wood!)
-stabilizer jack pads (plastic)
-wheel chocks (plastic)
-lighter to light stove/oven and water heater
-tire pressure gauge
I have also purchased my own personal stuff, plastic plates ,cups and bowls (4 of each for a couple bucks from WM), plasticware, organizer shelves, plastic bins for the water and sewer stuff, bedding, bathroom stuff (shower curtain, shelving, etc), rubber shelf liners, kitchen stuff (a lot of that I already had), and just little things to personalize it for me to feel like home. The list above is the stuff you really need to start with. As others have said, you will think of things along the way and can pick those up as needed. You will know more once you get your RV and see what you need and want. Dollar store and Walmart are good places to save some money (as long as you don't look around in there too long!
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You can also google "RV must haves". There are You Tube videos of top ten things you must have, etc. Some are gadgets you probably don't have to have at this point but some really good ideas and money saving tips. Good luck!