What are the prerequisites to make a PCB design with processor and other ICs interfaced?
Given your baseline of 1GHz ARM you are looking at a multilayer board (8 layers say) with a high pin count BGA package. An AM3539 is a 324-Pin PBGA package. Assuming you don't go package on package for the memory, you are looking at an awful lot of high speed interconnects, all of which have to be balanced and impedence matched. You'd start with a 5 grand licence for Altium Designer or something similar.

You can have a look at the hardware platforms like the Beaglebone and the Pandaboard which will give you an excellent idea of the scale involved. There are some terrifying videos on YouTube (example) showing you the routing involved with DDR3.

What I'm doing currently is designing a baseboard around a SoM - a system on module (A Gumstix). All the horror is taken care of, yet you have a lot of low level access to pins.