Majordan’s guidance is a good beginning. There is a philosophy held by long standing koi keepers that the only items to put in a pond are water, fish and food. You will get inundated by the vending community with stuff that falls into a category called elephant amulets. The fellow wears an elephant amulet to keep the elephants away where there are no elephants, and see it works.
As for a treatment kit, I keep several items on hand, partially because of my role in our club, and share some with the members because it’s too difficult for members to keep them. Other items are kept by everyone. Oil of clove is good to use as an anesthetic during treatment and when trying to catch the little critters. Salt from Lowe’s or Home Depot, the softener kind, is also cheap to keep and doesn’t expire. An api test kit is a must. A sock net is important for large fish to prevent injury to their internal organs, hydrogen peroxide is important for several uses and has a long shelf life. Beta dyne is excellent as a topical. Praziquantel is good and has a long shelf life, but there is another dewormer out, I can’t remember the name offhand, that is reportedly better. Dimilin is excellent for crustacean parasites. As for the stuff I keep on hand, that is kanamycin sulfate for non- injection treatment of infections. I am not an injection fan.
There are other items some folks use, but be careful. Potassium permanganate is effective but dangerous, as it is an oxidizing agent and can burn your fish in an overdose. Hydrogen peroxide will stop its chemical reaction. It works well as a dip or as a topical. I use terminate or pro form-c a lot. They are a mix of formalin and malachite green that works well as an antibacterial. Again excellent but can cause problems when overdosed. I use it in spring startup, in one quarantine technique, and as an occasional whole pond prophylactic treatment. Surgical scizzors, tweezers, and q tips are useful. There are also liquid bandages for topical treatment. Diagnosis requires a microscope that a koi health advisor in a local club will use to sort out your problem. Some buy their own.
As for the rest, you will need to talk to others. I’m not a fan of melafix, stress coat, and the myriad of other stuff some of which are in the amulet category. Fungicides, for example, are generally a bad idea in my opinion but that’s just me.