About Ac to DC convertor..?
Switched mode power supplies (SMPS) are the standard method of doing what you require. They are efficient, compact, light weight and, due to mass production, low cost.

See my answer to How does a cell phone charger work? for a brief overview of the operation and identification of the essential parts of an SMPS.

SMPS design is tricky and since mains voltages are involved they are hazardous and difficult to debug. You will not build one for less cost than a commercially available unit so I recommend that you avoid attempting this until you have advanced well in your electronics studies.