What goes first in the signal chain EQ or Compression?

Both are valid - you get different effects from the two signal chain orders. A lot will depend on your source material, for example, the amount of sibillance. Try both configurations and see which you prefer.

I'm not sure why this is in this forum - moving to pro audio gear.

nobodie's gonna spank you... but the way iwas taught and it makes sense to me is EQ/tonal fx first... second compression/dynamics... third time based fx... flangers/doublers/reverb.....

the basic premise is that some of what your gonna want to compress is tonal balance related so if it's not there in the first place (having been EQ'd out) you'll compress less... the same is true of ringing in your reverb forinstance...

Like any other engineer, I can't get enough of either. So I will equalize and then compress and/or limit. Sometimes compress and then equalize to track. And on mix down I may very well add additional EQ and compression or maybe compression and EQ.

Which is the right way?? Whichever way sounds right. Certainly don't do it the wrong way or it might be wrong and sound wrong?

I don't like wrong recordings. I like right recordings. But I also like left recordings. in fact I like it best when my recordings are both right and left not to mention center and nothing left behind nor right behind.

Sitting on my behind with little left or right
Ms. Remy Ann David