First you need to decide how much ripple your circuit can tolerate. If you want really low ripple, you'll need a couple of regulators after the caps. A 7809 and a 7909 should work out OK. If you use a 10VAC transformer or wallwart, you'll get apx 13.5V which gives just enough headroom for 9V regulators and a bit of ripple.
The formula for ripple is::
Vrip = I/F*C
Where Vrip is peak to peak ripple, I is the load current in amps, F the frequency in Hz, and C the capacitor in farads. This formula is only an approximation, and thus the actual ripple will probably be lower. Try a couple of 4700uF, 25V caps. Any of the 1N400x series diodes should work for this project since the max current is low at around 250ma or so.