Welcome!
I hope that kit didn't cost a lot, because you've been
pool-stored. You might have seen others be victimized in the store when you were there.... they're the ones with a huge pile of stuff the clerks are happy to wheel out to their car for them. Your pool doesn't have to be grossly expensive and difficult to maintain, no matter what the pool store experts tell you.
About that startup kit... The strips are at best unreliable. The 3" tablets will keep and have some use. The powdered shock may have some use, depending on which of three commonly used powders all of which are called "shock" it is. The algaecide is unnecessary if you maintain the chemistry, and the stain away is probably useless if you're filling from a municipal water supply. If you're on a well and you have iron, that's a whole 'nother thread.
If the pucks came with a floater, you can put them in now to get some chlorine in the pool. If there's no floater, don't use them. Keep track of how many you use.
What you do need is a proper test kit. For pool chemicals, you might need to raise or lower the pH, you might need to raise the alkalinity, you will need a source of chlorine without unwanted side effects, and you will need some stabilizer to protect the chlorine from the sun. The pucks have some in them, and the shock powder might, which is why I say they have some usefulness but that you should keep track of how many you put in. The good news is, you're starting fresh and what you need can be bought cheaper than the pool store.
I suggest you start reading in
Pool School until you feel like this.
Test Kits,
ABCs,
Recommended Chemicals,
How to Chlorinate, and
Poolmath are all worth reading early on. It seems like a lot, but once you have a proper test kit in your mitts and start
doing, it will make sense. By Fourth of July, you'll be an old pro and daily maintenance will be about as time consuming and complicated as brushing and flossing your teeth.
