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I've had good results with my Zoom H4n recorder. I believe the recent version of this is called the H4essential ($200):
https://www.sweetwater.com/store/detail/H4E--zoom-h4essential-portable-recorder
I've used just the built-in stereo condenser mics to good effect, but it also has two inputs for mics that you can use instead of OR in addition to the built-in mics. You can then import the digital file into your Macbook and use the free Garage Band for mixing and editing.
If you decide to want mics over and above the built-ins, companies such as Shure and AKG make some very good quality but affordable mics that would be more than enough for anyone other than the professionals. You could try a pair of small diaphragm condenser mics such as the AKG P170 (I see them online for about $90 each), or a large diaphragm condenser mic such as the AKG P220 ($130) depending on your particular application and taste (YouTube has lots of reviews and examples of miking pianos that you could browse to help you decide). If you want to capture the very low frequencies, you might add a kick drum mic such as the Shure PGA52 ($120) and mic the lower string side of the piano nice and close.
As far as video, I'm not as sure. I stick with my cellphone, which seems decent enough, at least when I remember to record on high quality settings. If you prefer a dedicated video recorder (as it sounds like you do), then I have no recommendations, other than to suggest you probably don't need to spend a ton; even the affordable stuff is pretty good these days.
Lastly, you might want to consider some soft box photography lights, which will help you capture some better video without weird shadows and such. You can pick up a cheap pair on Amazon for under $100.
Good luck!
P.S.: No need for a separate mixer. The Zoom recorder lets you select levels and has some built-in effects and other tools such as peak limiting. Then you'd just mix in Garage Band.
Enthusiastic but mediocre amateur.