A basic formula I memorized is:
Capacitance = 0.7 x Current / 2x AC Frequency x Vripple
where Vripple is how much you're willing to have the voltage go up and down on the dc output.
You have a 6v AC transformer ... that means the peak voltage is about 6x1.41 = ~ 8.5v and if you use a bridge rectifier you may have about 1-1.2v drop on the diodes, so you end up with a peak voltage of about 7.2v.
Now if you want a minimum of 6v, it means you can afford a Vripple of 1.2v
For example, if you want 0.25A output, 6v minimum and you're in US (so frequency is 60Hz) then Capacitance = 0.7x0.25 / (2x60x1.2) = 0.175/144 = 0.001215 Farads = 1215uF
Another simple formula is basically Vripple = Iout / 2fC (for a full wave rectifier)
... so as you increase the capacitance the Vripple decreases. For 1215uF, we have Vripple = 0.25/ 2x60x0.001215 = 0.25/0.1458 = 1.71 volts (so as you can see not quite 1.2v but both formulas are simplifications and give you a reasonable value)
You can basically lower the ripple by increasing capacitance, you don't have to resume to exactly these values.
Not sure for what you want this... if you want it to obtain a 5v power supply, you should make sure the dc voltage is always higher than 5v + whatever voltage drop the linear regulator requires. A 7805 needs about 1.5v , so you'd need a minimum of 6.5v at input.. a LD1117 or *1117 needs only about 1v-1.1v etc etc