What aspects of the vessel's capacity will time charterers usually be interested in?

It depends on the type of ship. For a bulker, for example, her deadweight carrying capacity (DWCC) and deadweight all told (DWAT). For a ro-ro ship, her lane-metres. For a containership, the number of slots (TEUs) and reefer slot numbers. They are also interested in the declared constant weight (a fixed tonnage allowed for water, stores, provisions, spares, etc. ).