The 50 vs. 75 ohm cable topic has been debated to death here and elsewhere. The short answer is that, according to bigger guns than me (like Bob Parness), this isn't a big factor on a receive only system, as the characterisitc impedience of a broadband antenna varies wildly over it's range.
What does matter is the quality of the coax, and the length of the run. RG-6QS (Quad Shield), such as is used in sat. dish installs, should work just fine for scanner reception. Don't get the RS RG-58 or RG-8 coax, it's low quality, high loss. Quality connectors and their proper installation is also important.
I'm assuming by "static", you mean poor reception, but you don't supply enough details - frequencies, distance to systems being monitored, etc., to make much of an evaluation.
I'd suggest that you get the antenna higher, at least 20 feet. And depending on the frequencies you wish to receive, you may need to get a better antenna. I'm guessing you are using the RS 20-176 antenna, which is really only good for VHF-Hi, in spite of the fact that it's has those two little spikes for 800 MHz that you mention. Something like a good discone (not the RS model, it's junk!).
Mark S.