Wiring and soldering a prototype board
There's a nice tutorial on using perfboards:
http://www.instructables.com/id/How-to-Prototype-Without-Using-Printed-Circuit-Boa/?ALLSTEPS

Basic idea is simple: place your components on the copper-free side, so that legs protrude through to the copper, to which you solder them. Try to place them in such a layout that you have to run minimum amount of wiring (especially on high-speed buses, such as SPI). Wire IC pins point-to-point, use joints to do multipoint wiring.

As for choice of headers - it's a matter of taste and wealth :) And application itself, of course. Since you mentioned audio jacks, I would assume relatively frequent plugging/unplugging action at least on the daughter board side. For that I would recommend putting headers on both sides of the board, so that you connect to both sides of the PI header as well, thus improving structural integrity a bit. You can leave those pins unconnected.