I obviously know what compression is, aswell as how it's achieved. But exactly how do you figure out your compression and design what compression you want from the get go? Aswell how does one decide on what bore, stroke, cam and head to get? I know bore and stroke all come down to your crank, connecting rod and piston but how does one know what they need?

 

It's even more complicated than just relating calculated C/R to fuel octane rating. There is "static" (calculated) verses "dynamic" (due to intake valve closing as the piston is on the way up) compression ratios.
The engine's C/R and octane requirements are as much determined by turbulence caused by "quench" due to combustion chamber shape as by just the calculated C/R.
Ideally, you want to run as high a compression ratio as you can without detonation, for a given octane fuel.
This is some good reading:http://speedomotive.com/Building%20Tips.htm
You should be suitably confused now ...