When on the radio I want the studio monitors to mute automatically when I open the mic (normal radio station stuff) so there is no feedback. I have read that some boards do and some don't but I can never find this info when reading descriptions. How can I achieve this?
You should be able to find monitor muting as a default or configurable setup on most radio consoles. Make sure you looking at sound boards that are specifically marketed as radio consoles. Something like this Wheatstone Audioarts analog console or this Lawo digital console. If not specifically called out in the features, you can also look for consoles that can trigger on air lights, as those contact closures can also be used to mute the monitors with some simple, inexpensive outboard gear. A Mackie or other inexpensive all purpose audio board isn't likely to have either feature.