Compressor or EQ first?
I almost always EQ after compression but I find it very helpful to have an EQ before the compressor in the signal chain too.
Even if you’re happy with the original tone an EQ can be used as a tool to drive the compressor in different ways.
Or on the contrary if you feel the compressor is squashing a particular frequency too much, you can use the EQ to cut this area to help the compressor to work on the rest of the spectrum.
Some compressors such as the FabFilter Pro-C 2 have this built in as standard.