I am new to the Google WiFi. I am going to purchase the 3 pack. I know I'll have to set up one of the Points directly to my modem so it'll act as the router (which will be set up on the main floor). Speaking of the other 2 points, can I place them anywhere in the house and connect my TV, PlayStation, laptop etc. using their Ethernet ports? These 2 Points won't be connected directly to the modem but would be connected wirelessly. Would that improve the connection with my TV or not since they wouldn't be directly plugged into the modem?
You can set the other two up as wireless-only mesh/secondaries, and yes, you can connect nearby devices to them through their Ethernet ports, and yes, this definitely will be better than connecting to them via WiFi, since it will eliminate one of the "hops" that traffic would have to take through WiFi. You can even connect an inexpensive unmanaged Ethernet switch to make more ports available.
That said, proper placement is really important. If the primary is relatively close to the center of your home (which is perfect), you'll want to place the two mesh secondaries one or two rooms away from it. Close enough that they can get a strong 5GHz connection to the primary, and then provide WiFi coverage to more distant clients. That may mean a secondary isn't right in the middle of where your TV, console, computer, etc. are. So, I would experiment with placement first by putting a secondary where your wired devices can connect to it through Ethernet and then run a mesh test to see whether it gets a "great" connection. If it does, leave it there and use Ethernet to connect devices in that area to it. If it gets a weak connection in that location, then you may be better off moving it closer to the primary and letting client devices connect to it over WiFi instead. You can test the effectiveness of both of these configurations using an end-to-end internet speed test from those devices to see which is really better for your situation.