> I'm trying to build a circuit that will detect 3 separate currents (DC)
> in three separate lines (12V) and energize LEDs associated with each
> line current
 
You also have the 0V available ? I would use a voltage divider down
to 5V (or whatever the Vcc of the PIC will be) and either use this
voltage as the PIC Vcc (to transmit on power-up) or to trigger the
PIC into transmitting if te PIC is already powered-up

> Right now I'm thinking RF modules and PICs on both ends of
> transmission

I would suggest the Rx/Tx pair made by Keymark, re-sold under
various names, and there are also Linx, Rayming etc). Google for
315MHz transmitter or 433MHz transmitter to find suppliers in
the US (315MHz) or elsewhere (433MHz)

I use them for PIC-PIC comms and have found them reliable to at
least 100m, using Manchester encoded character strings with a
pre-amble to settle the AGC

http://www.jaycar.co.nz/products_uploaded/ZW3100(mod).pdf

http://www.jaycar.co.nz/products_uploaded/ZW3102(mod).pdf

Another option is to use rfPICs for transmission, and you'll need
a receiver of course

> I dont know enough about PICs to decide which one or type to use
> How does one determine which one to use?

In this case you could use the very smallest or cheapest or most
conveniently bought at both ends. At the transmitter end, you need
at most just 3 I/O ; one to detect current/voltage, one to turn the
transmitter on (if you need to save power) and one to transmit the
data. By transmitting on power-up you could lessen the I/O needed.
At the receiver end, the PIC waits for valid data on one I/O and
then turns on an LED with another

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