weewx documentation provides list of compatible stations
Costs depend on your country - not all station types are imported into all countries - check with your local supplier
Just about all will operate uninterrupted - although you need to allow for spiders, storms, internet outages and so on - as per any IT project.
The location of the sensors will affect the accuracy of the readings - read various met office reports regarding height above ground, stevenson screens, distance from trees and white surfaces etc etc.
A logger of some kind will be required - most have a logger - so that recovery can be performed in the event of communiction failures.
Most station types have their individual quirks and issues - from Davis thru to FineOffset.
Only you can ultimately decide - and your decision may ultimately depend on local availabilty and support in the event of problems.