Which is the plant which puts out oxygen the fastest?

Terrestrial plants do not recycle inorganic CO2 fast enough to supply O2 for a closed ecosystem. Algae are the organisms NASA has used. This should give you a very rough point of comparison to the number of plants/algae needed to supply oxygen for life support.

Optimally "6 liters of algae water will produce 600 liters of oxygen, and consume 720 liters of CO2

http://www.projectrho.com/rocket/rocket3g.html

it takes "17.5 trees per person" to produce oxygen however 20 trees per person are needed to consume the CO2 per person according to NASA.

http://www.nas.nasa.gov/About/Education/SpaceSettl...

Plants have root & stem systems that are not photosynthetic so must be supported by the photosynthate produced by the leaves. Stems & roots require O2 for basal metabolism but do not generate the O2 themselves.

Algae has no dependent parts that use oxygen in cellular respiration like the plants so Algae generates far more O2 than the same plant mass.

there are many plants that can produce large quantities of oxygen. If I remember right from school from by weight the plant that produces the most is algae. Though if your looking for more common house plants sprouts, mother in laws tongue (snake plant) and Arcea Palm are amongst the best. Spider plants also produce lots and are much harder to kill than some others.

Ficus religiosa