I'm no expert, but here's what I think. There are others here who are more knowledgeable than I, and if they see this thread and respond, go with what they suggest.
First, read the manual. Compressors vary widely. For instance, some have auto makeup gains and some don't.
Looking at the picture with the four knobs, I'm guessing that the three knobs on the left are one compressor and the peak limiter knob on the right is a second compressor.
A peak limiter is sometimes referred to as a brick wall limiter; it sets a point past which it won't allow any more gain. Your gain staging and the first compressor should be sufficient such that a peak limiter isn't needed, or at most is there for safety. I would start by turning it off. The manual should say more about how this particular peak limiter should be used, but I'm guessing you won't need it or will need very little.
Initially, set the ratio around 2:1. Turn the threshold knob on the left all the way down to -40. If I understand your plan, while playing finger style, you'll want to raise the threshold until you just start seeing some gain reduction in the meter, then back off until there's none.
Now switching to slap, adjust the ratio until it sounds good to you, probably somewhere between 1.5 and 3 or 4 depending on how you play. You may then need to lower the threshold until the output level is the same for both finger style and slap. When you lower the threshold, you may need to readjust the ratio to keep it sounding good.
Then adjust the output knob to get the gain where it needs to be in the signal chain.
That's my guess without having read the manual and played through it myself. Again, compressors vary widely one from another and have different uses, so reading the manual can be helpful.