I set up two identical lead core rigs, and I couldn't be happier with how they are working out, especially for the money, these are economical rigs and are as close as the nearest wal-mart.
I used the ugly Stick Intercoastal ICCA 11761ML rod in 7'6" for the rods.
This is a med-light action rod that is rated for 10-20 pound test. What makes this a good rod for lead core is that it is long and soft, since it is designed for fly-lining delicate live bait like anchovies.
Why long and soft? Two main reasons. Long to get the rods out away from my kayak so I can troll both sides with more space between the lines. Long and soft to absorb the shock of the fish, since the lead core doesn't stretch at all. This is critical, as the fish have been larger and when you get up to the boat you really need the extra margin.
I have had seven colors out and the rod has enough backbone to not flex too much either from the drag.
I am using the Shakespeare Tidewater 30L, without the line counter. It holds 330 yds of 20 lb test, which is just about right for a 10 color (300 foot) spool of 12 pound test lead core.
I did not use backing, but there is room for a little, and it would probably be better for the line if you had it, plus give you some fighting margin. I have read that a level wind is important, although I have fished lead core on a non-level wind spool with no trouble.
I use about 20 feet of either 6 or 4 pound p-line for leader, tied with a small (#14?) swivel using uni-knots between lead and leader. Why so long? So that there is enough to stretch. I have been able to wind the leader right onto the reel no problem, but worry about a strong run that might hang it on a guide going back out. But so far it has worked great on trout to 7 pounds. I have also used short, under 6 foot leaders to avoid getting onto the rod, and that has worked as well. Back off the drag when you get the fish close...or else.
Rod, reel and line are all within feet of each other at wal-mart, together costing less than $100. Wind some 12 pound or so test mono on during the "non lead core" season and you have a great light ocean anchovy-tossing rig to boot. Just rinse and care for the reel religiously after using in salt, and don't expect it to be a shimano. loL
Hope this helps someone.