No simple answer, I'm afraid! As you noted there are so many different "opinions" on this and a shortage of facts. Probably the only accurate statements are from one cable to another rather than from spec to spec.
First on the solid copper versus copper-clad steel.. They both should work equally for signal transmission (all other things equal) due to the skin effect (signal migrates to the outside of the cable). The steel will offer more strength in bending but it doesn't carry power as well (satellite dishes require small amounts of power to be sent through the line to power the LNB's on the dish). Because of this, copper-clad is a specialized cable used only for signal transmission (but that's probably all anyone is trying to use it for).
As far as the quad-shield... The best I can offer is that it should offer greater shielding of the signal, but many times it really is only offering water/weatherproofing and, thus, makes the cost only necessary if it is buried or outdoors. Some people say that's what the "u" in RG-6U is, but u is not for underground but for whatever the manufacturer wants. There are many standards (and almost all end in U). So usually it means some variant of "universal" or multi-use -- which tends to include underground applications.
RG-59 and RG-6 have huge variance that can make many RJ-59's outperform the RG-6's and vice-versa. RG-6 only means the center is 18awg. RJ-59's could be 18, but usually are 20. Usually the difference is in the testing and manufacturing quality process, but you pretty much have to rely on the manufacturers for their info. If they lie you'll probably never know it. So manufacturers like Belkin (who has the best stuff out there) can have their stuff tested and then everyone agrees on its performance. Depending on the signals frequencies and levels you are carrying the specifics can matter a whole lot.
Check this article out too:
http://www.audioholics.com/education/cables/video-cable-shielding
You can figure out the best product at the best price point for you... As long as you don't run parallel to 110V power lines you'll probably be fine with what you've got. Make sure you can make nice connectors though, because that's where a lot of the actual signal problems arise.