Building a mains source power supply
The MUR410 diodes should work OK for you in this application, although you don't really need an ultra-fast diode for a 50/60Hz rectifier application. 

It is not common practice to provide short circuit protection to rectifiers in power supply circuits like you are building. However, it would be good practice to place a fuse in the primary circuit to the transformer. 

Grounding the case of the transformer is not a bad idea. But you don't want to ground the output of your power supply either at the secondary coil or the output of the rectifier(s) since most power supplies are used to provided ground-isolated voltages. Still, you should provide some connection means on the power supply to make the ground connection convenient on the occasions when it is needed. On commercial bench-top lab supplies this is usually done by including a green or black 5-way binding post which is electrically connected to the mains ground wire.