Should you put your EQ before or after your compressor? Or both?
Both EQ (equalizers) and compressors are tools for controlling signal levels. EQ controls the relative levels of specific frequencies; most often the levels set by the EQ are fixed at the one setting, not dynamic. Compression controls levels dynamically, in response to your incoming signal level; most often the levels set by a compressor are not specific to any particular frequencies- the increase or decrease in level happens to the entire frequency range.
There are exceptions: there are a rare few dynamic EQ units, and there are a number of compressors which can be set to affect only specific frequency ranges. Regardless of these exceptions though, it is important to understand the general principle of how equalization and compression are different, and how they can work together.
If you place the EQ first in the chain, then you can regulate the relative strength of different frequencies in order to get a less obvious, more consistent and natural response across all notes. This can be especially notable if you turn down the lowest lows a bit, since they have the strongest signal peaks. If you want you can instead create a more dramatic squish in a certain range by adjusting the EQ to feed higher spikes in that range into the comp. The downside of "EQ first" is that any later changes you make to the EQ, changing tones between songs for example, will affect the response of the compressor.
If you place the compressor first in the chain, that allows you to make as many dramatic changes to the EQ settings as you want, without having to adjust your compression settings too. The downside there is just that you may sometimes wish for EQ to adjust the balance of your low end and high end levels into the compressor.
So should you have two EQ's, both before and after the comp? It's not actually recommended because each stage can add noise and unwanted changes to your tone, and it all adds up. So sometimes the added control over your signal is not worth the degradation of the signal quality. You have to balance the benefits against the penalties with your specific gear.
To simplify and generalize, I'd say if you change your EQ settings a lot, you may benefit most from putting the EQ after the comp; whereas if you set your EQ once and forget it, then you could benefit more from putting the EQ in front.