What are the important design considerations when laying out a PCB?
I'm going to say "Location, location, location". You can make or break a PCB by selecting where the components go. Some (like switches, or transistors that have to be on a heatsink) may have fixed positions; but you can make a huge difference by moving the rest around until they are in the best place. Actually routing the signals is less difficult!

Some components call for placement close together to minimise the length of high current paths. That can also make the difference between a nice quiet board and one that fails EMC emissions tests.

Some components call for the right orientation to connect to their neighbours without all the tracks crossing over each other. Or enough distance between them to allow all the tracks to pass. And so on. 

Spend time placing the components, watching the "rats nest" pattern of unrouted traces, and simplifying it as much as you can. Make several trial placements and save them, and route the best. When you get stuck, move the problem parts around and start routing again.

It really does take practice.

Minor points : 


if the boards are to be hand assembled, there will be many fewer mistakes if all the ICs and polarised caps are the same way round!
if all the components are on the same side of the board, build is easier
you can simplify testing if every signal has at least one accessible pad (test pad or existing IC pin or socket pin) on the opposite side of the board...