Center tapped rectifier
Should be like this (the schematic is wrong, your diodes are shorting out the transformer and possibly preventing your caps from violently venting from overvoltage abuse):







simulate this circuit &ndash; Schematic created using CircuitLab

1N54XX rectifiers are pretty rugged, they may have survived, but I suggest using new ones because if they have failed they will likely fail short and can damage the ones that are not already fried. They're also really inexpensive. If you do try to re-use them, test them with the diode function on your multimeter before wiring them in. 

As noted you should use a capacitor voltage rating that is at least 20% ~ 30% higher than \$\sqrt2\$ times the RMS voltage of your transformer winding, so for a 24V:24V winding, use 50V caps. 35V caps are too close- the transformer will have a higher voltage when lightly loaded and the line voltage may be a bit high at some times of day. 

The capacitance you need will depend on your maximum load and the maximum output ripple you can tolerate. A good estimate of the peak-to-peak ripple is:

\$V_R= \frac{I_{load}T_C}{C}\$ with C in Farads, Iload in Amperes and Tc is 0.0083 for 60Hz or 0.01 for 50Hz mains using full wave rectification as you have.