Funny you should ask, the SO-239 ground plane is one of my specialties so I guess rather than refer you to a hundred previous threads I'll go through it again, briefly. (?)
OK, the radials are a small percentage longer than the radiator (not critical) so about 1/4" should do for putting a small hook in one end where it passes through the hole in the flange. The actual increased length is the distance from that hole to the center so you're OK there. Yeah, soldering is better than nuts and bolts.
For indoor use it's 14ga solid copper, 12ga is too large a diameter to fit into the center pin and I guess you figured out a good source is an old piece of Romex attacked with a sharp knife. For outdoor use it's 1/6" diameter brazing rod, soft copper wire bends easily in a strong wind. File the ends of the wire or rod and the solder blobs nearly flush with the bottom of the flange, more on that later. Then a gob of silicone bath tub caulk seals the gaps between the center pin and the insulating bushing and it and the main body of the connector.
Now you're ready to mount the wee beastie. Indoors a short length of 1 1/4" diameter pipe will hold it nicely, what to do with it next is for you to figure out. Outdoors it's ordinary TV antenna mast and whatever sort of brackets suit how you want to install it. Here's where it gets interesting, shove the coax through the mast before you put it up and screw it to the antenna just letting in hang on a couple feet of slack for now.
Next you waterproof it the good old fashioned Army way using a roll of cheap, like Wally Mort black vinyl electrical tape because it stretches a whole lot better than Scotch or the other expensive stuff. (I wonder if the Army figured that out.) Starting a couple of inches down the coax below the connector spiral wrap the tape stretching and holding tension as you go overlapping each turn at it's center (half the width of the tape) making sure it's all nice and tight, flat and even. When you get to the flange wrap a couple of turns right up against it (not over it dum dum) and start your spiral back down to just below where you started. Then wrap a couple of slack turns, that is neither stretched nor tensioned straight around the coax, snip and you're done. The idea behind those last turns is the tape tends to shrink back and separate so if you keep tension to the end you'll have a few inches of tape flapping in the breeze eventually.
I guess by now you figured out that by pulling the coax back down the mast the antenna flips up top and sits there looking all kind of cute without any nuts, bolts, baling wire, duct tape or other redneck means of holding it there. Remember filing off the excess radial stubs and solder blobs? Bubba forgot to do it and now his antenna sits cockeyed, he'll still be trying to figure it out a month from next Sunday so will one of you please give him a link to this thread?
One last thought, the radials should be at 90 degrees to the radiator or bent >slightly< downward, any more and it ceases to be a ground plane and becomes a coaxial dipole.
