you have a pretty good list there! just a few tips:
some things that should be in the grooming kit: rubber curry, metal curry, hard brush, soft brush, medium brush, face brush, face curry, mane and tail brush, mane and tail comb, and a hoof pick!
i would have some winter blankets too, not just a cooler. at least a sheet, medium, and heavy.
dont forget your bathing products - shampoo, conditioner, sponge, maybe another curry, towels, ect.
also, even though your barn supplies first aid supplies, its always nice to have some of your own. even just a bucket, some betadine/iodine/other ointment for small cuts, some towels, vet wrap, ect.
make sure you dont get any tack related items before you get the horse! you have to make sure everything fits the horse perfectly! this includes saddle, bridle, bit, girth, blankets, and stuff like that. you can buy brushes, bathing supplies, leadropes, saddle pads, and stuff like that before though. if your boarding barn doesnt supply water and feed buckets, you can buy them too.
also, dont forget that you may need some other "small" things for your horse because every horse is different..maybe polos, suppliments, boots, bell boots, special saddle pad (risers, half pads, ect.), and just and just anything else like that!
good luck with your first horse(: