I don't know what the sunset is on your bet, but chances are you will lose it.
You don't do 1GHz designs when you are at a point still wanting to understand how circuit boards work. You also don't do it without equipment, either.
You could do perhaps 10MHz or even 30MHz, perhaps... in some reasonable period of time spanning many many months if you are really, really sharp and can learn very fast and using modest priced equipment. I had no problems at all wire wrapping circuits that ran at 4MHz and 8Mhz, for example. And if you were really, really good at wire wrapping you might even do better than that. But not without a lot of practice.
Boards can be fabricated using low tech. Even Radio Shack (I think they still do) sells Ferric Chloride that you can use to etch boards. And you can use a laser printer to generate the masks. (You will need to go google things up for some helpful pages.) But these kinds of boards are no good at much more than the 30MHz I mention above. Everything starts to change around then.
And you expect to design a video graphics card from scratch? (Actually, depending on what you mean by that it could be fairly easy compared to the 1GHz requirement, as you can actually do it with a few output pins and a few resistors if you do all the hard work in software on the cpu -- see the maximite board design for details here.)
You will need to thoroughly educate yourself and perform an extensive survey of your options for your bet and then select the ones that will maximize your odds of completing them. Frankly, start by researching the 1GHz requirement and see what is required there. I think that is your show-stopper, unless you are permitted to limit it to the processor speed and don't have to do a bus that operates anywhere near that fast. Look for processors with internal PLL clock multiplier capabilities. And run the external bus to memory as slow as your bet allows you to do. 128Mb memory is not a problem if it is allowed to be slow. It's just money.
Good luck. I love lofty goals driving learning. And a bet is a fine way to go. But you have bitten off a huge risk in your bet.
And by the way, at 1GHz mere circuit diagrams are not the issue. Layout knowledge is vital. You are operating in wave guide territory. The PCI bus, itself never that fast, used reflection wave technology and crafted clock skew rules to achieve it's initial 33MHz and 66MHz capabilities and reduced power. And the tools required even to check a design were very expensive at the time. (Less so, now.) But you don't even know about that, yet.