Well - first, its important that some one teach you how to wrap HANDS ON. An incorrectly done wrap can cause way more harm than good (bandage bows, slipped / tangled wraps etc). Have your vet, an experienced trainer, or an upper level pony clubber teach you.
First essential “wrap” that comes to mind is a “vet wrap” that the stretchy, elastic, rubbery disposable wrap that is used for keeping wounds clean etc. It is also good for wrapping a hoof if needed. Your vet kit should have a few rolls.
I think every “horse person” should a set of “standing wraps” (also called stable wraps). These are handy for situations where you need to stabilize swelling in a leg, cover a wound, treat injuries etc. Standing wraps consist of “pillow wraps” and nylon, non stretch bandages on top.
In my opinion, that is all you need. Polo wraps don’t do much, shipping wraps need to be expertly applied, and its usually better to just go with shipping boots.
Do you have some one that can show you HOW to apply wraps? Its really an art and a science. Uniform tension is KEY and it takes a fair bit of practice to master.