Hi and thanks for using 2CarPros.com.
A plugged heater core will not make the engine overheat. Since you have a build up of debris in the cooling system, I suggest doing a flush again. Perhaps the debris was plugging the thermostat and not allowing coolant to flow properly. As far as a brand, discuss that with the people at the parts store. There are many to choose from, and from experience, they all do pretty much the same.
Here is a link that shows how to properly drain and flush the system. As far as replacing the thermostat, it needs to be there.
Let me know if this helps or if you have other questions.
Wednesday, October 17th, 2018 AT 5:44 PM