You don't need to buy three transformers to get +/- 5v , +/-8v and +/- 12v. It's possible to use just only one transformer, or two transformers, one for +/- 12v and one for +/-5v and +/-8v.
How big the transformer will be, it depends on how much current you need on each of those voltages.
Figure out how much current you want on each voltage, because that matters when selecting the transformer voltage and power rating.
For example, let's say 5v @ 0.5 A , 8v @ 0.5 A , 12v @ 1 A
Next, you should know by now that a linear regulator will need about 1-2 volts above the output voltage to get a stable output voltage, so for 12v DC you will need at least 14v at the input.
So you have transformer - > bridge rectifier -> capacitor - > 14v Input for the 12v linear regulator
Now if you go back towards the transformer. You know you'll have a capacitor that will smooth out the output of a transformer after the bridge rectifier so depending on how big the capacitor and the current you want there's going to be a fluctuation of voltage.
There's a simple approximation formula which can tell you how much voltage will fluctuate between a minimum and maximum ... let's ignore the 5v and the 8v for the moment and focus on just the 12v... which means we work with 1 Amp.
Capacitance = Current / 2 x AC Frequency x Voltage
In your case, capacitance = 1 A / 2 x 50 Hz (Europe) x Voltage. Let's say you're going to use a 3300uF capacitor or in other words 0.0033 F ===> 0.0033 F = 1A/ 100xVoltage ===> 0.33 Voltage = 1 , so Voltage = 1 / 0.33 = 3 volts.
So with a 3300uF capacitor, you have transformer - > bridge rectifier - > capacitor (14-17v) -> linear regulator , maybe lm317 or 7812 -> 12v
Now you know that pretty much every bridge rectifier loses about 0.8-1.4 volts so you should have a peak voltage of 17v + 1.4v before the bridge rectifier or about 18.4 volts at the transformer.
The peak voltage of a transformer is determined with the formula Vpeak = Vtransformer x 1.4142 so 18.4 = Vtransf x 1.414 therefore Vtransf = 18.4/1.4142 = 13 volts AC.
So your transformer should have a secondary winding of 13v AC or more to be able to get a stable 12v @ 1 A after going through bridge rectifier, capacitor, linear regulator. If you increase the capacitance to decrease that 3v of ripple to maybe 1-2v, you could work with a 12v AC transformer, which is more standardized than 13v AC or more.
Or, instead of trying to keep the voltage after capacitor to a minimum of 14v by using large capacitors (3300uF 25-35v capacitors are large and expensive), you could just use a transformer with higher secondary voltage, like maybe 15v AC, which will give you a peak voltage of 20v so you can have 14-20v DC with smaller capacitors, like maybe 1000uF 25v for 1A of current...
With a 12v AC transformer, if you want to get 12v @ 1A from it, you have the formula that sort of approximates it : VA rating = VA DC / 0.62 = (12v x 1A)/0.62 = 19.3 VA ... let's say 20 VA.
If you want +/- 12v @ 1A, you can get a center tap 24v AC transformer, and you'll have two windings with 12v AC and you're in business... a 24v center tap, 40 VA transformer. 50 VA would be easier to find.
Now all the talk above is for just +/- 12v 1A.
If you want to use the same transformer to get 8v @ 0.5A and 5v @ 0.5 A, that means you need a transformer that can also handle 1A of current for these two other voltages. You can use a linear regulator to like 7808 or LM317 to output 8v @ 1A , and then use a 7805 or LM317 to get 0.5 A from the output of the 8v regulator.
This means that the regulators after the bridge rectifier and capacitor need to have at least 14v @ 2A to do everything so you can adjust the math above (increase capacitor size using the formula and using 2A for current in the formula) and you'd also need a larger transformer, rated for around 75-100VA.
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