Advice on POE Switch and AP setup?

Hi all, I just moved into a 2-story house and got 1.5 Gbps internet. The modem is in the basement, but Wi-Fi signal is weak on the main and second floors. Every room has Cat6 wired in. From what I’ve read, two options are either adding APs or using a mesh system, with APs generally being better (but I’m open to opinions). The modem from my ISP doesn’t have enough LAN ports (1× 10G, 2× 2.5G, 2× 1G) for all my Cat6 runs. My plan is to add a network switch in the basement, connect all the Cat6 cables there, and then set up two APs (Ubiquiti ceiling/wall mounts? Something else?) — one on the main floor and one upstairs.

Questions:

1. Is this plan solid? Anything I should consider or do differently (AP vs mesh, switch setup, etc.)?

2. Which port on the modem should I use to connect the network switch (10G, 2.5G, or 1G)?

3. Since APs require PoE, what are some good PoE switch options that can handle 1.5 Gbps fiber and give me at least 6 ports? Thanks!