If your goal is to design a modern PC, forget it really.
Modern chips interface with busses like PCI express or high-speed differential busses. You can't breadboard this up, no way. Frequencies are from 100MHz up to several GHz. A breadboard will probably 'fall apart' at a couple of MHz (I can't even get my serial port to work at 3MBaud on the heavily used breadboard I got). Even routing boards with these speeds requires a lot of knowledge and know-how.
Other than that, the exact pin-outs of some chips are hard to get. Where are you going to find the pin-out of a chipset? How are you going to prototype this? Your question of an one-off motherboard an fairly cheaply is a contradiction itself. A one-off is not cheap, never will.
The DesignSpark toolkit is hilarious for any PCB more than 2 or 4 layers. You know modern computer motherboards use atleast 8 layers? There are some figures of like 12 or 16 I believe. You also know they are designed with multi-million EDA tools to verify signal integrity, PCB design, etc.? You also know that they are not designed by one person?
As a one-off these costs not hundreds to produce, probably thousands each (may even be underestimated). Only in production where ten of thousands are produced, they become affordable.
Anyway, if you intend to learn about the workings of a motherboard you probably should look the theory up of high-speed PCB design such as differential routing pairs and multi-layer routing, multi-phase switch-mode power supplies, phase locked loops, BGA's, power supply decoupling, seperate/local ground planes, and a bunch of other stuff. Most of this what I called can just be applied to PCB design. Th schematic is just figuring out what the pinouts are, how chips should be interfaces, power supply requirements and practical production requirements. As I said, pin-outs of some chips or the workings can be proprietary (however I do know you can find the Intel CPU's pin-outs on the internet).
Look, if we all could do this you would see projects all over the internet with people 'hey, that guy stuck a Celeron on his line follower robot!'.