Like they have said before, do your gating and corrective EQing first. As for EQ and compression, it depends on the use. Someone asked Dave Pensado about the order of EQ and Compression, here was his response.
1st ask if you wanna EQ the compressor, or compress the EQ. Think about this for a minute. Say you have a fat lo-endy kik. You don't want all that 60-80 triggering the compressor. So compress it first to bring out the knock, and EQ the lo end back in. On a guitar you might want to EQ it to get all the strings to sound, or to bring out a certain frequency, then compress it a tad to keep it in a certain dynamic range, or to bring out the attack. Remember, if you put the EQ 1st, then you have to reset the compressor everytime you make an EQ change. But always remember, there are no rules, just what sounds good to you. Experiment.