CPR Class ~ you will never realize the importance of that class until it's needed; I hope you never have to realize it. If you have a pool in your backyard CPR Training for you and the family should sit at the very top of the essentials list.
As far as "stuff"
The Test Kit and Speed Stir I think are mandatory.
If you have a Sam's Club local
http://www.samsclub.com/sams/150-gal-deck-box/prod8340178.ip
Mine came with lifetime warranty, they have now been reduced to 2 years, but in 5 years I haven't had a problem with them and they get full sun all summer and anything winter throws at them in Pennsylvania ~ I don't put them in the shed to winter. They look like they did the day I brought them home. They have not faded or warped. And they are high enough that you can use them "buffet style" if necessary for larger gathers.
I have a pole for vac and a pole for brush&net.
Spa tubing, I use that for hoses and now as port of entry to deep clean my sand bed in the filter so I don't disrupt the laterals.
Dedicated 2 gallon bucket and 5 gallon bucket for pool only.
My tool box has all my tools for pool only, lube, teflon tape, plugs, clamps.
Poles and inflatables have a dedicated part of yard fence that they are secured to. Some folks use a PVC stand for their inflatables, but we bungee them to the fence as we have very high winds.
Pair of girls/women's tights, some use a tube sock ~ I use a pair each year to introduce my granular CYA to the pool, I have a small bungee I attach to the pair of tights to place it in front of the return to let it disperse. This keeps the product off the pool bottom.
This year I am getting a "leaf cover" have fought the winter cover long enough (winds), so I am trying something new to see how it works out.
I am not a fan of pre-buying a bunch of stuff. I grew up with a pool so covered the basics; poles, vac, net, brush, found this lace ordered the kit and speed stir. We purchased and implemented as we went along and found out what we were into.