1) bog standard hair rigged mono (cut from whatever my mainline is at the time) but connected to the lead swivel with a lower breaking strain loop to form a weak point.
2) hinged semi stiff rig for pop ups
3) combi rig.
first one because sometimes you just cant beat going back to the start as i find it can and does trip up the beasties plus it can be used with all baits and most methods too.
hinged semi stiff rig with the hinge formed by peeling back the coating and a little tungsten putty added, i like to play with pop ups (and even fish with them sometimes) and the coated braid will make it harder for mr carpy to deal with. the ESP has a nice fine diameter and i find it easy to tie plus it will accept most knots too.
combi rig, why? i dont know really but i have 3 rods so why knot
my reel line at the moment is ESP olive in 15lb, pretty fine at 0.35 and is hard to spot when under water, sinks fast too, has good abrasion resistance and damned good knot strength and so it makes a good hooklink too, provided you build in a weak spot that is and so i use a short loop of 8lb to connect to the swivel, the hook will be a #6 or #4 armapoint ssbp or sssp in microbarb, sometimes with a kicker sometimes knot
hinged rig will be ESP two tone to a armapoint lsc micro or a gardner Mugga in #6 with the bait as a popup mounted either on a KD or a blowback rig.
lastly, i am currently experimenting with combi rigs and the one i am tying atm is with ESP stiff rig bristle with a two tone hooklink.
i take a #4 ssbp and a 6" length of two tone, strip the braid completely and form a knotless with hair, put on a kicker. take the stiff rig and put a 1" bend in then thread the braid thru the bend and whip 6 turns away from the hook eye, come back over the whips with two turns and back thru the bend the same way you go in, dribble and draw tight then cut off the tails, add tungsten putty to the whipping and then add a quik clip to the other end and steam straight. make the hooklink part as long or short as you need to. stiff section more or less ensures that your bait is presenting + it has the added benifit of acting like a spring to reset your bait after an aborted pickup.