Dual polarity power supply for project, possible choices?
Dealing with mains AC.

Some transformers are supplied with wire tails rather than tags.
 One of those will allow mains connection with a minimum of danger. Solder the two lives mains lead wires to the two primary wires and use heat shrink sleeving over the connections. This can all be done with the mains never having been connected. When you are finished there is minimal chance of electric shock. 

This does NOT include a fuse, which would be "good" [tm]  to have. You can buy inline  fuse holders which also have wire tails. You can do as above with Mains-fuse, fuse-transformer and transformer-mains joints, all soldered and all with heat shrink insulation. 

DO NOT just twist wires together.
 DO NOT use wiring twist on "nuts" which are solderless.
 The latter can be very useful but are a very very very bad safety start when you are not used to mains.

Clamp mains lead with a cable entry clamp or several cable ties through several pairs of holes or similar so that there is no way for external mechanical stress 
to be transferred to internal connections.



You can buy AC output plug pack transformers designed `for low voltage lighting use with ratings in the 1A to 2A range and voltages of typically 12 VAC to 24 VAC. This gives you a low voltage source of AC without having to deal with mains connections. 

Note that 12 VAC has a peak value of about 17 Vdc. Easily enough for a low current opamp supply and enough for a DC supply at the DC = rated AC voltage as long as a sensibly low dropout regulator is used. 

If you now use an eg transformer with a number of low voltage windings you can generate several windings. eg if you had a transformer with 2 x 24 VAC centre-tapped windings you can connect 12VAC to a 12V half winding and get 12-12 from the other centre tapped winding.

With a little Heath Robinson approach you can connect eg 24VAC across a centre tapped 24VAC centre tapped winding and then use the 24AC ct as 12-12. 

The above transformers may also have a mains winding. Insulate it before starting and ignore.

You can connect an AC voltage to a winding intended for equal or greater voltage. eg 12 VAC into a 12VAC or 15 VAC or 20 VAC winding. If the target winding is too much greater than the input voltage the magnetisation current will be too low and the core will not be well used. Often not a problem. 

You can ry connecting eg 15VAC to a 12VAC winding but the increased magnetisation current will drive the core towards saturation and even 15->12 is probably rather too much. If you try it and it starts to get more mildly warm you can probably disconnect without permanent damage. Probably.