Welcome!
First thing: order a proper test kit. If your wife is a clean freak, you'll need it. You can have water like this
Yes, that's full. There's an
article in pool school, but save some time and just head for
TFTestkits.net
With a fresh fill, you have zero chlorine. So you need to add some. You also have no stabilizer in tap water, so you'll need that, too. Initially, you want to add 2 ppm FC every day. That's about 5 cups of standard 8.25% clorox bleach. If you measure the actual water depth, we can get a better approximation of the pool volume and get even more accurate.
To add stabilizer, you need Cyanuric acid aka CYA. Get it at Lowes or Walmart of any other big box store with a pool section. One 4 lb canister will be just about perfect. How to add it is in
Pool School - Recommended Pool Chemicals
Lastly, you'll need to adjust pH. You need a test kit to do that. So don't hesitate on ordering a kit. It probably won't be too bad swimming in it before then, since you bathe in the same source water, but it will change over time, so that needs fine-tuning.
Low CH won't be a problem with a vinyl pool, and TA is the last thing you worry about, so they can wait for the test kit. They have to, anyway, since you need to know where you're at.
To decipher some of my terms:
Pool School - ABCs of Pool Water Chemistry
What to use to adjust what:
Pool School - Recommended Pool Chemicals
How much to use:
Pool School - PoolMath