Hi Craig,
I ran 20 - Amp circuit, only because I had the 12 - 2 Romex and breakers laying around.
A 15-Amp circuit would work fine with that amp.
So you will need a 15-Amp breaker (check to see what brand you have in your panel)
Roll of 14-2 Romex
See how long of a run you have, and see in you can buy a partial roll of Romex.
A full roll is 250" (that may be too much) I know the Depot has shorter rolls.
For the receptacle, don't buy the cheapest $.79 job, and get a same amp rating as the circuit you decide to run.
A good one is only a few bucks. Hubble makes some very good stuff.
Don't run a dedicated ground.
You just want all grounds to go to the same ground bar, and that ground bar tied into a proper ground rod system.
If you mentioned earlier about corroded ground rod connections; I'd add a bottle of Noalox
http://www.idealindustries.com/prodDetail.do?prodId=30-030 to your list.
Loosen your ground clamps and clean that area with a wire brush and coat the area with Noalox.