JoeN:
Instead of a homemade PCB, why not go half way and use a pad-per-hole solderable board, solder the parts down, make traces using hookup wire. It works fine and no mess, no having to make a PCB drawing, relatively easy to make changes with a little solder braid, etc. It's ugly, but you will probably want a case any way you make it.
I use stripboard, which works well with both DIP ICs and passive components, and is neater. When there are lots of digital connections to be made, I use a wiring pen for them.