I definitely want to echo Gary's initial comment about just grabbing a pen and paper and recording some readings of what you might be interested in. Personally, I track many QS things including sleep, food and other basic health-related measures. A good chunk is done manually. I do have a few "go-to" pieces of hardware that I rely on...
Here's my core set of qs tools. Nothing fancy:
* Braun digital ear thermometer
* Life brand spO2/heartrate monitor
* Paramed blood pressure/heartrate monitor
* Renpho wifi smartscale
* (not shown) Android Pixel2 smartphone
* (not shown) computer with Browser
The thermometer is a few years old. I'd probably choose a good quality no-touch version if I was in the market for one and had young kids.
The SpO2 monitor has been especially useful with our younger boy who suffers from asthma related breathing issues. He is prone to developing pneumonia and the monitor is an excellent indicator. We've had it attached to his finger while he's in the hospital with one of their wired SpO2 sensors and it's always within a percent or so. It doesn't have onboard history though, like some of the newer models that are less than $100 these days.
We only use the blood pressure monitor on my partner and me. I haven't compared the pressure readings with a commercial machine like the ones in the pharmacy or with a doctor's reading but the heart-rate component is very close to the SpO2's readings. (I find my fitbit Charge3's heart-rate readings spotty, btw).
The Renpho smart scale is basically a cheap option for a Withings scale. It syncs flawlessly with the app and tracks about a dozen weight-related metrics. It syncs the weight data to Fitbit really well. I haven't tried Google Fit.
(phone and computer) We log all the data for our whole family at EventLoggers.com (I'm the developer) and it displays nice dashboards of historical and summary data.