What to expect

my top items:
Progressive Industries EMS
Watts/or other quality adjustable water pressure regulator
Oxygenics shower head
X chocks
Reese or Equalizer WD hitch
Living in AZ you might consider a Hughes Autoformer since you will be using your air in low power situations
The rest will come to mind as you camp

Dealer hopefully will give you a starter kit. Use the cheap sewer hose until you figure out what works for you. People will tell you to buy a rhino sewer hose. Frankly I have seen more of them in the dumpster than any other brand. What ever you do, stick with a specific system. Get a multi fit elbow, connectors to join more than one hose and a decent hose support.
As for potable water hoses. Start with a 25 foot, maybe two. Get the 5/8 hose for better flow.
Electrical. Depending on the trailer, 30A, get a heavy duty extension cord and a few adapters.
Back on water, get a brass "Y" and a good brass regulator. You will never regret this.
Leveling. I like and use 2x6 boards cut about 24 inches. Cheap, durable, and if you happen to drive off and leave them, no big deal. I also have an assortment of 4x4s to use under the stabilizers.
Thats a good start.

bottle opener & corkscrew

Thanks for the speedy and helpful replies. The dealer is not including a starter kit so I am sort of on my own there. I think I might just keep my old sewer hose from my trade in ancient truck camper as the add ons are adding up quickly. I lived and camped in Oregon for 65 years and love to see a reply from my beloved state.

A good sense of humor and lots of patience.

Pencil and note pad.

Go camping. Write down stuff you think will make things easier, quicker or better.

Build extra shelf in garage at home to put stuff you buy that you end up discovering is not needed after all. That's where the sense of humor comes in handy.

Ohhh, I have this exact post already for you:
First Trip Essentials

I think I am going to love it here. So much good advice and the best is about attitude and humor. Having camped with horses for years I know about humor. Although I will miss my thousand pound camp friends, I know it will be much easier just caring for those of us with two legs. Thanks you guys

Yes, keep ALL your previous camping items from the horse trailer and see what works on the new camper. Then replace with new a little at a time as needed because of wear and tear.

Might consider a bottle jack.