The first step is to look at what kind of smartphone you have. If it is a newer Samsung Galaxy or an iPhone, you may have the answer right there. There are a lot of people using iPhones and getting both excellent video and extremely good audio.
Next option is if you have a laptop or tablet. Some of them have excellent video cameras built in and the audio isn't usually too bad.
If you will have a desktop computer in the same room (or even a laptop), an outboard webcam can be had nowadays for less than $100 that will give you 1080p video and pretty decent audio.
Beyond that, the sky is the limit. Zoom offers their Q2n, which is a fixed focus lens (no fancy video effects, no optical zoom, but with what Zoom calls Point Of View settings, which is essentially an electronic zoom. These tend to lose resolution and start to get pixelated or grainy as you zoom in. The upside is these are small and run on regular AA batteries. They also record audio extremely well. This has always been Zoom's strong point.
Zoom also offers their Q8, which is basically the same camera, but with some audio enhancements. The mics are removable and can be replace with task specific mic "capsules," probably of little or no use in a home environment. But the Q8 (which I have) also has the ability to accept two mic or line level inputs via an XLR/TRS cable. This allows you to use another source for your audio. The video is just OK. It's pretty decent in a well lit environment, but gets pretty noisy in anything less. The camera also has a fixed focus lens with only electronic zoom capabilities. The Q8 uses a proprietary battery and spares aren't cheap. However, if you have a USB battery pack for charging a cell phone, you can avoid buying spare batteries. Both the Q2 and Q8 will run from an external pack.
Another upside to both of the Zoom cameras is they will connect directly to a computer via USB and both the Q2n and the Q8 will function as a webcam on your computer. The mics can also be used with the webcam. A Q2 will run around $220. The Q8 is closer to $400.
I did a livestream with my Q8 back in May, which might give you an idea of the video quality. It's on Facebook and FB will only stream to 720p and not 1080p. The video quality difference between the two levels on the Q8 is pretty much negligible. The video is public, so you don't need a FB account to view it. You'll find it here:
https://www.facebook.com/paparaptor/videos/10222898014061857
The audio was done through a mixing board and the outputs were fed into the Q8 via the XLR/TRS connections. The audio quality wouldn't be quite as crisp and clear from the built-in mics.