No, APC does not shut your computer down, macOS does. The APC merely reports its status to macOS via its USB connection. That status includes things like the charge level, how many minutes are left before it’s out of battery power, the percentage of charge left, etc. macOS then acts based upon your settings in the Energy Saver preference panel. I have mine set to orderly shut down my iMac when the charge minutes left is down to 10 minutes. You first need to figure out how much power (watts) your system draws, then decide how long you want the system to last on battery backup (how long do outages typically last in your area), then select a model that meets those requirements. Well, and then there’s the budget considerations. The more power and longer battery time cost more money as the numbers go up.
As for which brands work with macOS you will need to check the manufacture’s specifications but most do if they have a USB port believe.
p.s. I also test the system occasionally to make sure it’s working. I pull the plug on the, UPS, observe that it goes into backup and then sit back and wait for the power to drain and observe that macOS shuts down my iMac correctly.