PIC Differences
Many of the PICs have similar naming schemes:
16F84 is the flash version - you can program and reprogram it
16C84 is the OTP - one time programmable - unless you feel like buying alot of these, steer clear
16F84A - a new (sort of) revision of the 16F84 - speed up to 20Mhz.
16LF84 - the L is low voltage - some of these things will run down at 2V!! (at 4 mhz)
the F84 is pretty out-dated. The 16F628 is cheaper, same number of pins, and I think it has more I/O but I'd have to double check. The 16F628 has a heck of a lot more hardward on board too!
Many programmers are still incompatible with the 'A' (ie 16F877A) revision of PICs. Check your programmer and software to see what PICs are supported.
IMHO the 16F628, 16F873A, and 16F877A are the core PICs for hobbyists. The 628 is great to learn on and the 873A and 877A have fun things like a large number of IO lines and A/D converters.