Expanding on the PSU suggestions, any electronic tool would be a good start and build your tool kit... A simple ESD (Electro-Static Discharge) circuit would be super easy...
It can be made from a 1/2"x1/2" square of copper clad board, a strap to hold the board against your wrist, some insulated wire, a round wire terminal and a 1M Ohm resistor. Cut the wire, anywhere, and solder the resistor to each of the two pieces. Solder the board to one end of the new cable. Attach the wire terminal to the other end of the cable.
The terminal is attached to earth ground. Remove a single face plate screw from either a wall plug, or light switch, place the wire terminal on the screw and screw it back in.
The copper pad is held against your bare skin, on the bottom side of your wrist, with the strap. Wear the wrist band/board when you are working on sensitive components...
That would give you something to practice soldering on and be useful... But, the real meat is in finding out why you might need it and why a 1M Ohm resistor is required... I will leave that to you...
If you think that you will be working with controllers, like the Arduino, or Raspberry Pi, you might want to build a TTL Logic Probe... It is also simple to build and would introduce you to comparators... I built this one:
http://www.neufeld.newton.ks.us/electronics/?p=31I also suggest checking out the YouTube video series that NASA made on soldering...