Raymond,
First, C2 and C3 are in backwards. The + side of the cap should go to the higher voltage, not to GND. Depends on the capacitor technology, but most polarized caps will be destroyed the way you have them. Could be spectacular, and not in a good way.
Next you need to know the output voltage of the solar cells, and know that a lead acid battery will need about 14.5V to be charged. They are called "12V" but they are not. So the solar cell output must be more than 14.5V plus the linear dropout voltage, which is about 2V for the LM350, plus a bit for drop across the FET. Say, 17V.
As was said, pick either linear or switcher. The switcher should be fine without the linear in front of it.
Lee