In retail, you won't find transformers with lots of windings on the secondary side. Usually, linear power supplies use custom transformers with up to 4 separate windings and join them together using relays to get voltage only slightly higher than the voltage you want at output, so that there's little voltage drop across the regulator (or pass transistor in case of a linear power supply).
I would suggest going for a 18-20v transformer, either with center tap, or with two separate windings of 9-10v on the secondary side.
One with two separate windings such as one of the below would work great:
http://uk.farnell.com/pro-power/ctfc50-9/transformer-50va-2x-9v/dp/1780856http://uk.farnell.com/pro-power/ctfc75-9/transformer-75va-2-x-9v/dp/1780861As they're separate, you can connect them either in series, or in parallel.
In series, you get 18v AC rms at 50 VA or about 24V DC after rectification and about 1.9A of current.
In parallel, you get 9v AC rms at 50VA or about 11 V DC after rectification and about 4 A of current.
If you connect a side of both windings together, you can just switch between the other two windings sides to get 9v AC rms or 18 v AC rms but then in both cases you only get a maximum of 1.9 A of current because a winding would be unused (wasted) when the switch is on 9v.
Either way, you can use 0.1uF 50v capacitors (but you should use 100v rated), you can use more easily available 35-50v electrolytic capacitor.
The 50 VA will give you will have 2 x 9v windings, each of about 2.78 A of current (after rectification and conversion to DC), that's about 1.8A
So if you want some voltage less than let's say 8v at 1A, you switch to single winding/both windings in parallel, and you have 11v max at input, the regulator needs about 2-2.5v to work properly therefore 8 + 2.5v < 11v and everything will be fine. Your regulator will only dissipate (11v - 8v) x 1A = 3w and everything is right with the world.
You still shouldn't use those 1n5422 as they're too weak, just use regular diodes with 0.6-0.8v forward voltage (rated for 3-4A) or bridge rectifiers like this one:
http://uk.farnell.com/multicomp/gsib1504/bridge-rectifier-15a-400v-gsib/dp/1861524Yeah, you get more forward voltage drop but who cares...