For me, my main "secret sauce" tool is a good compressor. I personally prefer colored over sterile transparent compressors. My preferences are the likes of: FEA Optifet, Diamond Bass Comp, EBS Multicomp, Lusithand Alma, Effectrode LA-1A, Drybell Module 4, Cornerstone Zefiro Optical Comp, Vox Snake Charmer, etc.), but then there are two transparent ones that I use which are absolute champs and still sound amazing for what they do: Boss BC-1X and Empress Bass Compressor. I previously owned the Becos Twain, which is in a league of its own, but it was TOO transparent for my taste.
As for EQ pedals, I like: Sadowsky preamp (for a refined 2-band eq), Aguilar Tone Hammer, EBS Microbass (either II or III), Whirlwind Bass Ten, and I especially like the API TranZformer LLX. That pedal is just top-notch studio quality!
An overall super-secret tool for me is my tried and true Zoom b1on. This thing hands down is my all-time go-to. If I could only keep one pedal for life, this is it.
As for DI pedals, I have not tried enough of them to yet form a solid opinion, although the EBS Microbass series is a safe bet for me every time. I would love to try any of what I call the "big boy" tube DI boxes: Arkham Oracle, Noble, Caveman Audio, etc.
Oh, and before I forget: Mad Professor Electric Blue Chorus (first version). Although this is a chorus pedal, this little thing adds a really cool stereo/doubler type of effect to the tone. Some people don't care for that but it's part of that tone that I constantly have in my head.