You'll get no disagreement from me about the advantages of a neat breadboard. I effectively stopped using solderless versions years ago, except for the simplest and temporary projects. For solderable boards, I usually use something with THP contacts arranged similarly to the solderless boards. Layout is easy using Eagle, and one gets schematic capture that way too.
Here's an example done years ago without PTH: (attached)
My preferred wire is 24 AWG with Kynar insulation. Insulated wire allows "trunks" to be built. Kynar avoids the ugly burn/melt back of PVC wire.
Yes, stretching annealed copper wire will make it straight. I just roll it on the bench with my finger. However, I interpreted this thread to be about solderless boards in which the wires are re-used.