How are bridge rectifiers rated?
I guess the \$\times\$3 rule of thumb refers to the transformer's secondary voltage, the AC voltage before rectifying. If your output is 18 V DC then the transformer will be a 14 V type. That 14 V is the RMS value, peak value is \$\sqrt{2}\$ times higher, or 20 V. Subtract 2 diode drops and you arrive at 18 V.  

So applying the \$\times\$3 rule to the 14 V already gives you 100 % headroom, applying it to the 18 V gives you almost 200 % headroom, which is overly cautious IMO. Since 20 V is the highest voltage to expect all three will do fine.  

The current is a different story.  



If the smoothing capacitor is charged the input voltage will be too low for the greatest part of the cycle to make the diode conduct. Only for a short period you'll have a current that recharges the capacitor. So you can expect a large current peak there, several times the average of 1 A. A 1A diode like the 1N4001 can handle this current, though it's a good idea to have some headroom here as well. For a 1 A output a 2 A diode is a good idea, so 
also for current all three rectifiers will do.