If I want to tiker with one isolated component that has not too much pins (let's say less than 40), I use a breakout board. When more is involved it becomes impractical, because you have to hook so many wires from the breakouts to the breadboard that the mess turns it highly probable that you'll make a mistake.
What I do sometimes is make a "partial" board, in which I have the high-density components interconnected and hook just their ends (usually one or two SPI ports) to the breadboard.
I do the boards myself on the first design round, and have it fabbed when I arrive to the final design - or sometimes when the prototype board is too complex and I'm unable to make it myself.
I know two good ways to make PCB at home. One is with toner transfer paper and the other is with photosensitive PCBs.
With the first you print your PCB to that special paper using a laser printer, and then press this paper against the board using a heat source (can be an old iron). After that you use water to wash out the paper and the toner is attached to the copper, ready to etch.
With the photosensitive board you print the circuit to a transparent sheet, place it on the board and expose it to UV light; then you apply a developer and again it's ready to etch.
The first method is cheaper (assuming you already have a laser printer) but I found the limit for vias to be about 0.5 mm. With the second you can have 0.3 mm.