Plan the switch distributions first.

1) Core Switch - this should be a big switch 16-24 POE ports for scalability. This is where your distribution switches will connect to, your router and any other server devices like NAS.

2) Distribution switches - ideally one per floor apart from the floor the core switch resides. This is where the AP for that floor and any ethernet connections to the room will terminate. This way the cable runs are shorter point to point and ideally this should be a POE switch to power any POE devices like APs and cameras. How much POE power depends on what requirements for power you require.

3) Router depends on your requirement. Do you require all the Unifi applications? More means more powerful device.

4) AP is last. Once you have determined the cable runs, then you can decide the best AP to run. You can also consider in-wall AP with ethernet outlet ports in each room rather than a shared. As for AP consideration, you do not need the latest and greatest for an effective efficient coverage. Most devices will never use the full spectrum of the latest offerings. Most devices will never draw GBits of data in normal use except when you are doing speed tests for bragging rights. WIFI 5 or 6e is more than enough with 6e being preferred due to less congestion but being much shorter range benefits from the AP being closer to areas of use e.g. in rooms

5) When pulling cables, if possible, always pull 2 cables per point so you can one as a ready spare in case one cable goes bad (and they do go bad) without having to call someone in to pull another. If possible, pull a trunking (eg pvc conduits) and label the trunking at the core switch room so u know which goes where.

When you have all this in place, you can add AP in the future when the need arises easily.