Yes, the actuator cable does have to be heavy enough to carry the current, I don't know what gauge it should actually be, maybe someone else who knows for sure will help out and comment on that. My 9' dish came with a roll of new wire that sounds like what you threw out, I used that, it has two coax and three wires for a servo, three for the motor/actuator. The motor wires on mine are pretty thick, that run is 50'. I have the same type wire on my 12' dish as on the 9', that run is 120'. The actuator/motor wires measure .12'', whatever gauge that is I don't know. The signal and ground wires are half that.
This dish is the 10' CM in your signature?
Probably the best would be to look and see what's on different sats and see if there's anything you like. Lyngsat has lists:
http://www.lyngsat.com/america.html
The site I use the most and find easiest to understand is Sathint:
http://sathint.com/america
Here in CT I can get down to about 55W and then I'm into trees, if it weren't for trees, I could probably get down to about 30W. Going the other way, 127W is my furthest receivable sat. I'd think in South Carolina it'd be about the same for you, about 30W to 129W, depending on the terrain, trees,etc. You'll want to get the dish set in a place where it can see as much of the arc as possible if you can, almost all sats have at least one or two channels worth getting. Look on Sathint, Lyngsat, etc, and get an idea of what's up there, also keep in mind that channels come and go, even if nothing's on a sat today, that doesn't mean there won't be tomorrow!