12v AC 50 VA transformer
full wave rectifier => 12v x 1.414 = 17v DC peak voltage.
Current = ~ 0.62 x 50/12 = 2.58A or easier ... 50va / 17 which gives more or less the same result. Let's say 2.5 amps.
Bridge rectifier forward voltage max = 1.1v , let's say 1v. So peak dc after bridge rectifier = 17v - 2x1v = 15v.
50.000 uF is A LOT. A basic formula for capacitance is Capacitance = Current / 2 x ac x Vripple. Your transformer can do maximum 2.5 amps , the ldo only needs 0.5v above 12v to work but use 1v for safety so do the math for a minimum of 13v at input, so you can afford 2v ripple.
Capacitance = 2.5 / 2x 50 x 2 = 2.5 / 200 = 0.0125 F or 12500 uF
That's for about 2.5 amps. If you think you're not going to use BOTH 5v and 12v at 1A at same time, then you can use lower capacitance. You're not going to exceed 2A if you use two LM2940. So 50000 uF is kinda pointless, excessive.
I would use 2 6800uF 35v capacitors and be done with it.
Use 35v rated capacitors or even higher, they'll last longer and handle currents better.
Also always worth keeping in mind that at low loads transformers often output higher voltage than the label ... check the transformer's Reg % column .. for the 50% it's 9%... so at low loads the output of the transformer could be 13.08v AC or about 19 volts DC. Still low enough to use 25v rated capacitors but 35v rated capacitors are not much bigger.
As for fuse ... 50 va / 230 = 0.217 ... I would probably use a 250-300mA slow blow fuse.
later edit : I would use the TO-220 version of that linear regulator, as it makes easier to put a heatsink. At 1A, you'd need a heatsink even for the 13-14v in , 12v out regulator.