Tom
As I understand it, partitioning a hard drive is really a throwback to early PC times when the OS could not support large drives and could only address smaller chunks of data. So, we had to partition the big drives down into smaller chunks. Now, all that stuff is in the past, so the only reason to partition a drive is if the user feels more comfortable with smaller working areas. However, you can achieve just the same thing with a well thought out folder structure.
Splitting up your OS, Lightroom, caches etc into different partitions will make no difference whatever to the speed at which the processor and RAM can access the data - they are still on the same physical volume. The only way to make an impact on this is to split them over different physical drives, internal or external. If external, there is no point in putting the drive on USB 2, it will be too slow. eSATA is what you need. The additional drives must be at least as fast as your present internal drive or faster. SSD is the way to go for screaming performance.
Another important point with conventional HDs is that the outermost rim of the disk is the fastest. So on a blank HD, load your speed-critical stuff - LR, Caches, catalog - first, preferably each one onto the rim of a separate drive. Sounds crazy, but you could use multiple small-capacity but fast drives for each chunk of data and really burn some silicon
For the PC, at any rate, a utility like HDtune is essential to bench-mark your drives so you can see what transfer rates and access times you are getting. Then you can optimise your IO and put stuff like the catalog and the CR cache in the places with the best speed.
John