Which biome has the most plants on it

Some trees (which may not be present on every planet) yield plant fibre when cut down. Just use your matter manipulator.

Vines work as plant fibre. You can find those growing on cave ceilings. Cut them with the matter manipulator, too.

You can grow some yourself, which is renewable, but takes some time and requires some preparation. You'll need a few seeds (you start with those) and basic stone tools.

According to currently available sources, farming is not affected by any external factors (soil type, rainfall, biome, temperature etc.). The only factor that affects plant growth is the growth rate of the particular crop. Toxic Tops require roughly 280 growth cycles, whereas Wheat only requires 27 cycles (a growth cycle represents the interval at which the game calculates growth, and is 20 seconds).

Taken from the Starbound Wikia site: http://starbound.wikia.com/wiki/Farming

Obviously, as the game is still in beta, there is room for this to change.