First thing you do is make sure it's full and the pump is running and there are no leaks. Let it run at least half an hour before you do anything chemically. Skimming, vacuuming, and struggling to fold up the cover is okay.
Then run a full set of tests. If you're nervous, watch the
videos. Test everything. You don't know how much stabilizer, if any, was added last year. If you post the results, someone should be along to advise you within an hour or so. Also, let us know what the water looks like. A clear pool requires a different approach than a green chunky pool.
As far as shopping ahead of time, about all I can recommend is a few gallons of plain bleach until you have readings. You know you'll need that eventually. You might need acid to lower pH, or you might need Borax to raise it. You won't need both, so don't buy both yet. You might need Baking Soda, but how much depends on test results. So that has to wait, too. So does CYA. Low Calcium is no problem with a vinyl pool, so you'll never have to buy any Calcium increaser.
We'll get you through this. No matter how yucky the pool has become, there's no reason it can't be crystal clear and sparkling before Memorial Day. And you'll have the chemistry mastered and find the whole daily routine pretty boring by Fourth of July. You'll also likely become a pool snob by then, too, and avoid other pools that don;t meet your standards.