Depending on the size of the fish you're targeting I would think that 80lb. braid would suffice with a double palomar to a 170+lb Owner ball bearing swivel. 100-200lb. flourocarbon or copolymer
http://www.p-line.com with Uni-Knot connections to both your swivel and jig should work. Make sure to melt the tag ends of the uni-knot so that it can't pull back through the knot. However that deep you may be able to just tie the braid directly to the jig with a Uni-Knot since it is so dark that deep. Make sure to upgrade the split rings on the jigs as well as using a solid ring above the split ring to tie onto. The 7/0 and 9/0 monster stinger hooks from Owner are SWEET!
http://www.river2sea.com saltwater jigs are just as beautiful as the shimano butterfly or lucanus jigs, but are half the price.
As far as rods go I just got the 200lb version of the Shimano Trevala. It is the diameter of my steelhead rod, but has the backbone of a pig stick and it helped me pull up a 300+lb grouper in Naples, FL! It is a great rod. The XXH version has the option of a gimbal butt that fits into a fighting belt with the cross pin for ease of pulling up most anything from the depths.
http://fish.shimano.com/publish/content ... ional.htmlOthers may have better ideas so keep researching, but these knots and rigs have done me right!
Tight lines!