Best Option for converting & processing multiple analog data lines
A good option would be something like the dsPIC33FJ64GP802, or one of it's family. This particular one has up to 13 analog inputs and can do 4-channels simultaneously (it has 4 Sample and Holds) It can sample up to 1.1Msps. It also has 8-ch DMA which takes the load from the CPU and makes things very fast if used correctly.
Here is the ADC part of the Family Reference Manual which will tell you a lot more.    

Instruction clock speed-wise, it can go up to 40 MIPS.