Welcome to the forum! And congrats on the first horse. Honestly, my first horse was a surprise by my non-horsey mother so all I had was a brush, a hoof pick, water bucket and one bag of feed (BIG SIGH!). Thankfully I've learned a ton since then and here's a complete list of what I believe everyone should get before buying a new horse--especially their first horse! ;)
Let's start out with a grooming kit...
-Grooming Bag/Tote or Bucket
-Jelly Curry Comb, Rubber Curry Comb and a Metal Curry Comb
-Hoof Pick (Get two! In case you lose one)
-Eye Drops (Get eye drops made for horses!)
-Hoof Dressing like Rain Maker
-Wash Clothes (Get 14 and wash weekly)
Tack: Hold off on any riding equipment until you have your horse. You want to make sure everything fits your horse perfectly!
-Halter (Get a nylon and a rope halter)
-Lead Rope (Get one for each halter)
-Splint & Bell Boots
-Lunge Whip or Carrot Stick (both if you'd like)
Get any necessarily feed and supplements before buying your horse. Depending on the age, senior? Junior? Alfalfa pellets? Cubes? Oils, etc. If I were you I'd get atleast 1 month's worth of hay prior to bringing him/her home.
Also get one tube of wormer in advance and stock up on a few extra salt blocks.
One thing to remember is you will want to save up for annual shots, vet checks and teeth floating and of course the occasional emergency visit/lameness exam.
Farrier needs be be done every 4-8 weeks, but a general 'rule' is every 6 weeks. Trimming and keeping the horse barefoot will be cheaper if you take care of their hooves properly, but most people get shoes which is more expensive depending on what your horse needs.
These are just the basics and I hope it helps you! :)