I would have to say that the PIC18F series is very common these days in many applications.
But, the 16F877 is a good place to start learning. If you are just starting out, or even moving from a high level MCU set-up like arduino to a low level, the 16F series is probably the best place to start.
The PIC16s have the basic functionality without the limitations of the PIC10 series that would run a beginner into trouble. Once you get a hang of the PIC16's you can scale up or down easily. And you don't need USB support, several UARTs, hardware multipliers, etc if you are just starting out.
If you are just getting into PICs, I would suggest the PICkit3 + dev board combo:
http://www.microchipdirect.com/ProductSearch.aspx?Keywords=DV164131It's the best bang for your dev-kit buck. And you can develop on the PIC18 board it comes with and scale up or down to your project as needed.
As for software, MP Lab is about your only choice. I would stick with the HI-TECH C compiler, but that is just my personal opinion. I always thought the HI-TECH C was better than Microchip C.