Re: building your own transformer.
It certainly can be done,& has been done,way back in the early days,but I feel you should buy a ready-made transformer.
A bought one must meet Electrical standards or they can't sell it,but you have only your own opinion that your homemade one is compliant,so
if you make a mistake in the primary side & blow up anything in your house wiring,your Insurance Company may wash their hands of it,& you may be in trouble with the Electrical licencing authority,&,as an Electrical Engineer,you don't want that!
Quite a few people rewind secondaries,but very few mess with the primary side.
The voltages you are talking about are fairly standard,so you can buy a transformer off the shelf.
If you want to run electronic equipment from your supply,there is a lot more to it than just a transformer & rectifier.
I suggest you Google under "power supply.",or have a look at some books.
VK6ZGO