As with all presentations, the lure you will be throwing (in this case jig head + soft plastic = lure) will determine what rod and reel you should use.
Before proceeding, let's make sure we understand one thing, when we say "shakey heads" we can actually be talking about two completely different things. For instance, about two summers ago, I threw 1/2 oz shakey heads with MAGNUM Zoom trick worms, hopping them as fast as I could along the bottom. Two of my bigger fish for that year came on that shakey head, a 7lb and a 6lb largemouth. I threw this presentation on a 7'6" Heavy Rod with 50 lb braid.
I assume, however, that when you say "shakey head," you are probably talking about the more finesse type of presentation that is most often associated with this technique. If this is the case, you are probably talking about 1/8th oz to 1/4th oz jigs plus 5-8 inch flat sided worms, craws, hula grubs, etc. If this is the case, you will probably be looking at the following set up: Around a 7ft, Medium powered rod with an extra fast or fast action. You will probably want to pair this up with a 2,000 or 3,000 sized reel. the line can be anywhere from around 6-12lbs.
I prefer the medium sized rod because it allows me the most sensitivity and control over this weight range of jig head (around 1/4th oz jighead) and lure. It also gives me enough of a backbone to REALLY set the hook on a fish. This is especially important with many of the shakey head jig heads out there, because the way they are designed often causes them to either get stuck in a fish's mouth, or not go through completely on the hook set. For this reason, I like to have a good enough backbone to drive that jig head through the fish's mouth. Also, I almost always set the hook upwards instead of sideways so that the head of the jig head does not interfere with the actual hook. Don't ask me how I know this, as I cannot tell you the number of fish I have lost on a shakey head setting the hook diagonally rather than straight up.
As far as line, I mostly go with 8lb fluorocarbon as it gets the bait down to the bottom, and gives me an incredible feel of the ground composition. I think fluoro is especially important with shakey heads as a finesse presentation because you will often want to work them on kind of a slack line so that your bait creeps and shakes along the bottom. In my opinion, fluorocarbon's sensitivity, ESPECIALLY on a slack line as is the case here, simply cannot be matched.
Now, if you want to go with a super light, finesse type of presentation for your shakey heads, you can go with 1/16th oz-1/8th oz jig heads and really small finesse worms. When the bite gets tough and I need a fish, a 1/8th oz jig head with a zoom finesse worm is a killer combo and it almost never fails to produce for me. If I am throwing this light of a lure, however, I will usually go to my Medium Light powered rod, with an extra fast tip, 2000 size reel and 4-6lb fluorocarbon. This is also a great setup when fishing rivers that have a lot of small fish.
Anyway, in conclusion, the presentation you are employing should dictate what size rod, reel, and line you are throwing. That could be anything from a 7'6 Heavy rod with 50lb braid, to a Medium Light rod with 4lb fluorocarbon line.
PS. I know you didn't ask about jig heads, but it should be worth mentioning that there are a wide arrange of jig head options. I mostly use the flat, "spot hopper" type of jig head that stands worms perfectly up. Other good options are round ball, or football jig heads. This is another topic for discussion when talking about jig heads. Good luck and have fun! ---Carlos