I ended up buying RG-8x, and two solderless connectors: one PL-259 and
one BNC. Also bought a nylon rail mount, which turned out to be an
ordeal in and of itself. No matter how much I tightened the thing, it
kept slipping.

I ended up drilling a hole through the bracket and into the rail into
which I put a machine screw. That seems to have done the trick.
Connected the solderless connector on the radio end; seems good to go,
but who knows. Went to do the antenna end and realized that the sales
guy at West Marine gave me a connector for a smaller cable and I
didn't check it at the store! Drat.

I know you guys recommended against the solderless connectors, but I
couldn't find a pre-made cable with a BNC on one end and a PL-259 on
the other and I sure as heck have no clue on how to solder anything.
Looks like I'm going to Boater's World tomorrow to see if they have
the solderless connector that I need. Debating whether to ditch this
rail mount and get a solid suface mount instead to attach to the side
of my console.. This piece of crap rail mount was $30.