Building a regulated power supply AC-to-DC
Option 1: A linear power supply:


transformer (at least 50 W output at 12 ... 15 V)
bridge rectifier
filter capacitor
fixed voltage regulators (78XX series)
some 0.1 ... 0.33 uF capacitors
optional: some rectifier diodes (to protect regulators in case reverse voltage is applied - if you charge batteries with the supply)


Option 2: A switched mode power supply. A 50 W transformer is quite big and heavy, and with the current configuration there will be a big energy loss as unwanted heat. A SMPS is the most effective solution, but you shouldn't build it yourself. There are online services that allow you to create almost any configuration and order the required parts.