Saturation is the fastest way to make a kit or a bass sound bigger, and the fastest way to make it sound small. The difference is rarely the amount of drive. It is whether the saturated signal replaces the original or sits next to it.
Why parallel
Saturation does two things at once. It adds harmonics, which is what you want: a bass that reads on a laptop speaker, a kick that has an edge. And it compresses, because a curve that bends the loud parts is a compressor whether you call it one or not. On the insert, at any serious drive, you get both, and the second one eats the transients you were trying to make bigger.
In parallel, you keep the original intact and blend a heavily driven copy underneath. The transients come from the clean signal; the density and the harmonics come from the driven one. You can push the drive much further than you ever would on an insert, precisely because it will not be alone in the mix.
The practical consequence: set the drive for character first, ignoring how much it crushes the signal. Then set the blend for how much of that character you want. Two decisions, two knobs, in that order.
Which model, for what
Not every saturation curve suits every source. The three examples below run identical plugin settings, drive at 65 %, and pair each model with the source it suits. Only the blend changes from one to the next, and that is the subject of the next section.
Drums. Tape rounds: the transients soften and the whole kit sits back a step, which is what you want when a loop arrives too spiky. Transformer saturates where the energy is, so on a kit it works on the kick and leaves the hats almost untouched; this is the one that glues a drum bus rather than colouring it. Transistor squares: hard front on the snare, a short clipped knock on the kick, for when the kit needs edges rather than weight.
Bass. A triode is asymmetrical and puts even harmonics above each note, which is exactly what makes a bass readable on small speakers without getting louder. A pentode holds clean longer and then bends hard on odd harmonics: the note keeps its low end and grows a growl in the mids, the sound of an amp working.
808. A sine-like sub has almost nothing above 100 Hz, so a phone plays almost nothing. Fuzz builds a whole ladder of harmonics on top of it, and that ladder is what a small speaker reproduces. It is the most extreme example on the bench, and the one where the blend matters most.
Where the mix knob should sit
Each example opens at a dose that works on that source: 40 % on the kit, 20 % on the bass, 15 % on the 808. Push the MIX to 100 % to hear the model alone, then bring it back down and listen for the point where the harmonics are still there but the transients have returned. That point is usually lower than people expect. On the 808, 15 % is already a lot.