Chassis - Grip, weight, and weight distribution is in the chassis file. You can then best match desired performance to the car. I prefer the chassis to be as close in dimensions as the original.
Suspension - The suspension ranges for ride height and springs are very large. For instance, the ride height is from 0 to 255. Each suspension file gives a limited range rather than the full range. By swapping suspensions, you change the "0" point on the ride height scale and you get a different upper and lower limit to the springs. For instance the BMW CSL ride height setting of 0 is the same as the BMW V12 LMR ride height setting of +15.
Body - I only find it useful if you don't have the car you want (like a chrome line car or something). Otherwise, it's best to start with the car you want and swap everything else onto it.
LSD - The LSD is set up differently for each car to give them a distinct feel. Although the ranges are the same across the board, it is like the suspension in that the values are relative to values set in the LSD file (which cannot be accessed). In addition to handling behaviour, the LSD also provides the engine braking character of a car.
Transmission - Like the suspension, different transmissions have different upper and lower ranges for each gear. So, yes, you can pop a 6 speed into a car, but you want to be grabbing the six speed with the ranges you want.