Since you went directly from closing to the home (and I'll take you literally that it's a new house, as in newly constructed):

1. Utilities was a great suggestion.

2. New house = no window coverings. (Unless you're immodest) sheet(s) or blanket(s) handy to tack over selected windows (and, of course, the means to attach/hang).

3. The movers most certainly haven't delivered your stuff yet (or, you haven't had time if you're moving yourself, since made B-line from closing to home), so a sleeping bag or air mattress or ??? to make your night on the floor minimally comfortable.

4. A roll of toilet paper.

5. Change of work clothes, toiletries kit, and a bath towel.

6. Cooler with ice to keep a few things (e.g. a celebratory six-pack) until the 'fridge gets delivered/hooked-up .

7. Of course, you were confident that it would close as scheduled, so you already gave the post office your change of address.

8. Check hot water heater, light it if it's not already cranked on.

9. Check to make sure filter has been installed on furnace.