What is the fastest growing plant by amount of carbon stored in the wood? Bamboo is one of the fastest growing woody plants (by height), but it is mostly hollow, and so I'm not sure that it stores that much carbon, relative to other plants.
Ecologists refer to this as 'gross productivity' and define it to be dry weight plant matter per area per year.
In temperate climates this is likely to be a grass. Switchgrass has been proposed as a bio feedstock, both because it's highly productive, and the plant pulls most of the necessary trace nutrients back into the roots in fall.
Poplar and willow are two other bio feedstocks. They reach maximum productivity when coppice grown, and harvested when stems are about 1" thick. (Grow on about 6" spacing)
Bamboo is a contender in more tropical climates. Note that it can be invasive.
Peatmoss is a contender for a different reason: All the temperate ones mentioned will reach a steady state fairly quickly (under 100 years) where the rate of decomposition matches the rate of production. But peat bogs are often saturated and acidic. This interferes with decomposition. Peat bogs will increase in depth as long as they remain wet. Peat bogs in Britain date back to the end of the last ice age.
Additionally peat requires very little besides air and water. Bogs are very poor in nutrients. In principle to sequester more peat it may only be necessary to place a low dam cross the outlet of a bog raising the water level a foot
If you aren't limited to land use, you can likely do better with algae. They produce very fast, but also decompose fast. You have to figure out some way to rapidly harvest the biomass, and remove enough water to frustrate the bacteria. This may make it an impractical solution.
(One of the proposed solutions to carbon sequesterization is to 'fertilize' the oceans with iron. In most water this is the limiting element. The notion is to create an algae bloom. When the algae die, their corpses settle to the abysal plain where decomposition is very slow. So far the experiments to test this aren't conclusive.)
One way to look at it to compare like with like is to look at the photosynthetic efficiency since carbon is fixed through photosynthesis.
By this measure, sugar cane comes on top, converting about 8% of the incomming sunlight energy into stored carbon energy.