Do you have composite, component, s-video or coax from the box?
Composite is a single (usually yellow) RCA jack. Component (or RGB) consists of three RCA jacks (red, green, blue). S-video is a single input that looks like a computer connection. Coax looks like cable TV.
Component is the best. S-video is next. It's a toss-up between coax and composite.
Do you have composite, component, s-video or coax on your TV?
Do you have composite, component, s-video or coax from the satellite dish? My guess is coax ... a 150 foot run probably won't matter much if it's coax.
I'm a little confused with what you mean by "cable box". Do you have cable television AND a satellite receiver? Or are you calling the the receiver/decoder a "cable box?"
With s-video you might get a little degradation (attenuation) at 150' ... you can get an s-video signal booster from Radio Shack. I don't know if they actually work.
You can learn a lot if you just Google: composite component svideo
Here's a site to get you started:
http://lyberty.com/encyc/articles/svideo.html