Carbon capture and storage in salt domes or in inactive fields is seen as an appealing option to meet the ambitious objectives of the Paris Agreement. Captured CO2 emissions can also be injected in active fields to enhance gas or oil recovery. We examine the optimal scale and timing of these different capturing and storage options in a dynamic model of an economy subject to a carbon budget. We consider the socially optimal outcome as well as the outcome under laissez-faire. The social optimum can have different forms depending on the initial carbon budget, the fossil fuel resource stock and the stock of already injected CO2 in active fields. The level and convexity of the costs of capturing, storing and producing renewable energy plays a role as well. We specify the conditions under which each possible sequence of regimes - no capturing, only enhanced recovery, only storage without enhanced recovery, a combination of both or only renewables - occurs. We quantify our analytical results by calibrating the model and running simulations.