How long ago did the 'paleozoic' era begin?

That would be 251 million years ago.

The end of the Paleozoic era marks the beginning of the Mesozoic. The last period of the Paleozoic era was the Permian, and the first period of the Mesozoic era was the Triassic; hence the extinction event (the biggest extinction event in the earth's history), the Permian-Triassic extinction, which defines the border between the eras.