I'd run the wire in the channel under the door sill trim, along with all the other wiring. Gauge depends on how much power you're supplying to the sub and how far the wire run is. I have a small amp on a 10" sub that's two feet from the distribution block, and I think I'm running 10 gauge.
I installed a sub in WCJr two weeks ago. I ran the amp power-on signal and RCA wiring under the door sill trim. I have a center console in the truck with heavier wiring and a relay, so I tapped the amp's power off of that - because I designed the circuit for an eventual amp along with powering the Cadillac seats and a little inverter. If I didn't have that already I would prefer to run it under the door sill trim because it's more protected than just running it under the carpet.
You must be registered for see images attach
You must be registered for see images attach
You must be registered for see images attach