Hmmm, well ...
Frankly, considering the current state of affairs, that really is an unproductive approach.
Whatever I may have done in the past - and I have (built power supplies) but it was a long time ago - this is simply no longer a viable approach.
As you will find in all consumer appliances, switchmode power supplies have taken over and for very good reasons. They are efficient, they are small and lightweight and now they are cheap. The bulky mains transformer is now more expensive than the sum of components in the switchmode supply.
So you do not start with a mains transformer, you use a switchmode supply from input to output. But the design of switchmode supplies is anything but trivial and it is extremely inadvisable to even consider it without considerable electronics engineering experience.
I suggest this project is a "dead duck". What you actually need is readily available and quite cheap. Possibly even cheaper second-hand from the "thrift" store. Have fun with the mental exercise here, but don't try it in practice.