240 V AC to 5 V DC power supply recommended fuse
5 V at 1 A gives an output power of 5 W. 

Assume it is 50% efficient (conservative) this gives an input power of 10 W.

10 W at 240 V is 10/240 A = 1/24 A any fuse around 0.1A would be enough if you can find one that small.

You should not need another capacitor across the output of that supply. In fact some supplies have a maximum allowed capacitance on the output.