John Bryant wrote an excellent article on the use of RF chokes to "sanitize" your coax:
http://www.dxing.info/equipment/coax_leadin_bryant.pdfThe article discusses different core materials, and provides equations on designing chokes for your frequency of interest.
I have a similar installation as Chris on all my coax lead-ins, except that I use a smaller FT-140 type J core and RG-174 coax. The RG-174 coax is terminated on each end with a PL-259 connector. I then use a female-female coax adaptor to connect the choke in between the coax lead-in and my antenna switch.
It's a worthwhile experiment to see just how much unwanted signal your coax will pickup on it's own, with a short between the center and braid at the remote end. In my case I found a significant improvement with only a single choke near my radio, as the choke outside at the antenna didn't make much of a difference. Also, I didn't bother with the separate ground on the shield remote to the radio.
If you use coax as a lead-in for your longwire, you will also get a huge improvement if you use an RF matching isolation transformer to connect the coax to the longwire. This is a lot easier to do than it sounds. John Bryant also wrote an article on this topic:
http://www.dxing.info/equipment/impedance_matching_bryant.pdfYou can also use Minicircuits transformers to do the same thing, with no need to wind anything.
http://www.minicircuits.com/products/transformers_pic_a.shtml Bruce Conti has an excellent tutorial on the construction of these isolation transformers. I've built several for DXers using the Rubbermaid baby food container as the housing, and this made the difference between hearing mostly noise to actually logging some real DX.
http://www.bamlog.com/diyxfmr.htm