There are a ton of embedded processors, but the PIC is a very popular chip family. They have literally hundreds of variations, so you can usually find anything you need.
Don't be too daunted by the huge datasheet, you don't need to know most of that stuff to effectively use the chip in this application. The latest MPLAB X has all sorts of plug-ins that make creating code easier.
My usage of the PIC has just scratched the surface, I used other microprocessors when I was gainfully employed and did a ton of processing with them.
Rubbing elbows with the analog side is all good, you need to have some background in that to avoid pitfalls, even in digital circuits. 
