Whew, nice list you have started there!
I just went through this myself about 5 months ago when I bought my first horse, and I'm STILL finding things I need for her! lol
Besides what you have listed, you'll also need...
* Bit (if you don't know what the horse used before and you're riding English, you usually can't go wrong with a thick Eggbutt Snaffle bit) - you'll need to measure your horse to see what size bit he wears if you don't already know
* Horse Toys - jolly ball, lik-it, etc. (I know, sounds silly, but you don't want to end up with a horse who's bored in his stall and develops bad habits like cribbing!)
* Helmet/half chaps (for you, and depending on the discipline you ride, but since you mentioned "crop" in your list I'm going to assume you ride English, as I do!)
* Fly mask (optional, some people don't use them)
* Dewormer (check to see when the last time the horse was given dewormer was and what type he was given) - this time of year, a lot of people are giving an ivermectin-based dewormer like this: Zimecterin® Gold - Horse.com
* Nolvasan antiseptic ointment for cuts and scrapes (goes with your first-aid kit, but I mentioned it specifically because that stuff is awesome!)
* Bucket (to go with your shampoo/bath kit)
That's all I can think of now off the top of my head - you have a good list going there, and the only other thing I'd say is to get a couple saddle pads...they get dirty fast and also you never know which will fit best with your saddle/for your horse
Congrats on the new horse, and good luck!!!