Go to the chat box and click the wheel in the top right corner, select Options. You can check or uncheck what ever you want to show. You can also create and name multiple tabs.

As said above, you can already do this. I have two chat boxes that I can switch between. One enables zone chat and one disables it; other than that they are the same. Though I'd love to hear 'LF help with WB xyz' I just can't tolerate the drivel, guild ads and annoyance of keeping zone on. I also turn 'say' and 'yell' to medium gray so they don't jump out. The only thing I can't disable via the chat box is 'system'. Unfortunately, that spams every single log on / log off of everyone on my friends list. So I fixed that by taking my friends list to zero and keeping it that way. Those who I really consider friends are in my guild so no loss.

I also wish there was a way on console to turn off, say, only one guild chat, or zone chat. It's either everything or nothing.

Yes, this is desperately needed.

I think as a matter of course, people need to start listing their platform. Console players take it for granted that people know they're talking about consoles, and PC players take it for granted that everyone plays PC.