You should ask your ISP if it’s possible to use your own router without their modem. This would be ideal, but it’s also probably fine to keep their modem if necessary.
As for which router/access point you should purchase, it’s really a question of budget and the area you are hoping to cover.
Personally, I’ve found Ubiquiti Unifi gear to be rock solid, and they have a lot to choose from depending on your requirements. They constantly release software updates with new features and security patches, which is far from guaranteed in consumer-grade routers, which often have very short support periods.
This is their cheapest all-in-one solution with built-in Wi-Fi for a very reasonable price. They have a lot to pick from, though, and as long as you disable remote access, they are very privacy-friendly working entirely locally.