I have ethernet throughout the first floor, I am not sure I think probably 6 jacks or so, I only use one that is wired to a computer I have setup. The 2nd floor does not have ethernet but has coax, but I think I will skip all the WiFi up there for now. The house layout is probably pretty standard, I would say 2000 sq ft first floor, 1500 square foot 2nd floor, and about 1500 square foot in the basement.

Once the first floor is complete, I will either run some ethernet, or run the MOCA method through the coax. Other option is just use the jacks on the first floor and point the AP up to the second, not sure how well that would work though

I would have no issue with an AP after a Unifi gateway, and a UniFi switch though, correct? If so that is the way I will go