Hi, Looking at the pics, On the transformer it looks like your 2 black wires are the 115v and the 3 wires are what's called a center tap configuration. You will have to measure the voltage at the 2 green wires, If it is 24v then you can ignore the middle wire (green/yell)
if the voltage is larger then you can use only one side of the winding for 24v (eg: one green and the green/yell) wire.
The bridge rectifier needed will have to handle the 10 amps plus a bit more. Pick one that is say, rated at 50-100v 15-20A.
You capacitor will need to be at least 10,000uF and 40-50V.
Hope this helps.