I use White Whale as my main 4-part trigger sequencer which gives as much control as I’d want over chance, patterns randomization, etc. I’m no reinventing the wheel, but it makes for straightforward programing of a kick/snare/hat/misc part.
With all of the quality kick modules, I usually just go straight for that rather than patch a kick from scratch. (usually the TipTop 808 or Plaits)
For snares/hats/claps I like to use a versatile noise source (personally, the SSF Quantum Rainbow), shaping it with the Hexinverter Galilean Moons and modulating the attack/release slightly to avoid a colder machine gun effect.
I often like the fourth part to be a snippet from Phonogene to add some variety. Generally, it doesn’t even matter what the source material is… if I trigger the playback of a small grain of it along with the beat it gives it some subtle personality.