The "basic" ingredients are just that -- basic. For a typical supercell, you need convective/potential instability, wind shear, and a forcing mechanism. Of course, there are a myriad of complicating factors that can enhance or detract from the supercell threat for a given environment. In addition, remember that supercells and the environments in which they occur are a continuum -- so there really are no concrete "magic numbers" for any of the "basic ingredients".
I'm not sure that I entirely under the "moisture" requirement/ingredient, since I think it's usually inherent in the instability factor. For example, you probably won't see significant CAPE in an environment with temperatures in the 80s and dewpoints in the 20s (unless the lapse rates are dry adiabatic from the surface to the tropopause LOL). You can play around with parcel moisture and see what it does to CAPE... You will see that moisture is inherent in any instability parameter that compares the parcel trace to the environmental profile (such as CAPE, LI, etc). Moisture is inherent in the LCL, but the LCL is more the result of the dewpoint depression (or RH, etc) than the magnitude of the dewpoint.
The "trough in the west" notion isn't really a requirement per se. Southwesterly flow over the Rockies leads to pressure falls in the lee of the mountains (for reasons that involve both thermal and vorticity processes). Given high pressure to the east, the pressure gradient force will result in southerly (-ish) flow across parts of the Plains. In most cases, this increase moisture across the same area, assuming there isn't strong ridging in the Gulf or a previous deep continental air intrusion. With southerly (or southeasterly) flow at the surface, beneath the southwesterly flow aloft, shear tends to be favorable over the same area. Southwesterly flow off the higher terrain leads to the development of the dryline (generally speaking!), which is a forcing mechanism that tends not to be very strong. In addition, the orientation of the flow aloft relative to the dry line tends to lead to a deeplayer shear vector that is not parallel to the dry line, which favors the development of discrete convection. A couple of studies coming out of the IHOP 2002 field project also indicate significant boundary layer rolls or undulations across drylines, leading to local areas of enhanced updrafts and downdrafts, which may help explain why discrete convection is typically favored on drylines...
With cold fronts, the situation is often quite different. Because of the thermal wind relationship, winds aloft are often parallel to the cold front, leading a shear vector that is oriented nearly parallel to the front. This leads to storms that move along the front, though it also leads to precipitation seeding downshear from the original convection. In addition, forcing along fronts tends to be strong. With strong forcing, shear vectors and deeplayer flow parallel to the front, etc, you can see why linear convection tends to be common on cold fronts, while dry lines tends to produce discrete convection.
As for the "exhaust" criterion...This may be slightly inherent in the other "ingredients" as well. Strong upper-level divergence creates updward motion and low-level convergence. This upward motion through a deep layer results in the column cooling, which tends to steepen lapse rates and helps remove the cap (both of which can increase CAPE). In addition, the surface convergence can serve to initiate convection, though upper-level divergence itself doesn't usually initiate surface-based convection since vertical motion resulting from even strong upper-level divergence is still only the order of a few cm/s. The upper-level divergence can, however, enahnce surface pressure falls and intensify/deepen surface low pressure cyclones, or enhance frontogenetical frontogenesis.
It's pivotal to remember that these are the most basic ingredients. Low-level shear, which is generally regarded to be a requirement for low-level mesocyclones, can vary greatly over a small area. Sometimes, everything looks conducive for the development of tornadic supercells, but they fail to develop. Other times, an unforeseen surface boundary (e.g. shallow OFB) can create enhanced low-level vorticity (baroclinically-induced vorticity) which can then be ingested by a supercell. In addition, storm mode has shown to be very important in whether or not there are tornadoes on a given. Then there's the LCL height and low-level instability (which can lead to enhanced low-level stretching of horizontal vorticity that is tilted into the vertical)... Finally, if we knew exactly what was "required" for tornadic supercells, the SPC would have a 100% PoD and 0% FAR.
