is it a above ground "easy set" style or a "real" pool?
We have an easy set one, we take ours down each year instead of winterizing it and have never needed to shock it. The only supplies we've needed are chlorine, skimmer net, brush/vac, floater for the chlorine tablets (unless you use powder), thermometer, and we found we often needed ph increase (ph+). Also if your just starting out I found the little dip style water test strips to be a lifesaver! Also since were in the north east and prefer warm water

I bought a solar cover for ours... a GOOD one from the pool supply store vs some cheapie from wally world. We trimmed our cover to fit perfectly in the pool (edge to edge) and use that as our cover. Keeps the water sparkly clean, and holds the temp overnight.
Oh, 1 more thing we found was a lifesaver... we use our Christmas lights timer on the cord for the filter pump. This way the pump goes on and runs for a few hours overnight and stays off during peak electrical rate hours. Sometimes we run the filter while the solar cover is on and its hot and were not in the pool to help circulate and heat the water even faster.
Make that 2 more things... if it's an easy set you may want an extra filter or 2. We often rinse ours out a few times before replacing to help save $, but they get filthy pretty quickly so we only rinse them a few times before tossing. We also use the anti fatigue mats under the ladder, this way kids rinse their feet before jumping in (keeps the water cleaner). You can kind of see them here: