Welcome and congrats! Great question! Click here to view our Visual Encyclopedia of Equipment - and scroll down to the section called Cleaning Tools.
I suggest you buy, if you don't already have:
1x TFP
suggested test kit see this page. For new pool owners, I only personally suggest two test kits in the entire world, the
TFTestkits TF-100 and the Taylor K-2006C. It might be tempting to go with a cheaper test kit or strips, but it only takes a pool going green once, or someone getting an ear infection once, before a real test kit would have paid for itself. Not to mention it will allow you to follow the TFP procedures to spend as little $ and time as possible on your pool, and more time in it!
1x pole - since your pool is quite large, a telescoping one is probably best, some have 1 telescoping segment, some have 2
1x hose of maybe 25ft if skimmer is in middle or probably the 50ft one
1x vinyl vacuum head *not plaster head* - there are some that are better than others, as shocking as that may seem
1x nylon/soft bristled brush or premium wall whale brush *not hard metal brush* - size is up to you, 18 or 24 inch are most common
1x leaf skimmer (not "leaf rake") or premium deep fine mesh net (will get smaller debris but is harder/slower to pull through water)
These items can be purchased online, at big box retailers like walmart in pool/bbq/garden areas, at pool stores, hardware/home improvement stores usually in garden section, and other places. I suggest you at least look at
this site's page to get an idea of what some very nice products are and what fair prices are. They even have
a bundles page with some deals for people like you. I suggest that site because their chemicals are the absolute freshest you can possibly get because they sell so much! That site is good to this forum and helps keep the lights on too. I don't personally get anything whether you shop there or not, but if you buy a Taylor K-2006C (or smaller versions Taylor K-2006/Leslie's 81329) from an online or retail store - please please please check the dates on the chemical bottles. Too many people have purchased a "new" kit that was sitting on the shelf for 2 years and the chemicals only have a couple months left...what a waste. Stored indoors, in a cool dark place, a fresh test kit should be good for 2 or maybe three years! So be careful and smart.
Lastly, your pool will need certain chemicals,
here is our Pool School page with links on how to chlorinate (sanitize) and what chemicals we suggest for what chemistry adjustments. Most pool store chemicals are identical to generic chemicals available at big box/hardware/grocery stores at much lower prices. We don't like wasting money here. We prefer to eat better food, donate it, host a pool party, invest for the future, etc.
If you live somewhere where your pool will be attacked by infinite leaves I can give suggestions for that.
I hope this wasn't too long - this is what I would have wanted someone to tell me in your situation. Let me know if you have any feedback or questions and I (or someone else if you prefer) can answer them!