P0420 code is something that you see often on the 8th gen Corollas - unfortunantly, there is no single component that seems to be more at fault than others. Basically - you will have to examine the entire EVAP system, which can be quite complex and take a good portion of your time. It is within the reach of a DIY - but you will need the factory service manual, some specialized equipment, and atleast a few hours to do the complete test.
I would check the parts instead of just blindly swap parts. You could do that - but many times you will tend to overlook the underlying problem end up replacing good components.
Just do a search for that particular code or EVAP issues, especially on this forum, will turn up a ton of info that might be useful.