Well, I've never seen such symbols for voltage regulators but
that's ok. Your schematic will not work because capacitor is
wired wrong. It should be accross bridge rectifier output.
It also should be 10-20 times bigger. Other than that everyhing is ok.
You could cascade regulators. This is specially prefered if
current draw on 12V is low but on 5V is high.
Some regulators really should have diode accross regulators input
and output to protect them. I guess it doesn't hurt to put them
anywhere.
Following should give you an idea.