How to avoid rookie mistakes while designing a PCB?
Probably too general a question to make it here.

The only cure for lack of experience is getting some experience. 

Step one, make sure the schematic is right. A perfectly implemented board of a schematic with errors or omissions is not going to be perfect.

Step two, verify that the board matches the schematic. If at all possible have somone else who is qualified take a look at it with new eyes, as it's very easy to think something does what you think it does, when it actually does something else, but you stopped actually seeing what was there 3 revisions ago and see what you think is there instead.

If you have mechanical constraints (you mentioned "components too close to edge of board") make a drawing that identifies them, and then make a drawing of the populated board, overlay, and make sure they are met. Draw from as many directions as you need to be sure you have checked, or model the thing in 3D. 

Trace widths - other than when messing about with high frequency stuff that needs specific widths for specific impedance, be as generous as you can, and also be aware of which ones are carrying 10 amps and which ones are carrying nano-amps so you can allocate the available space when they compete for it.

Take your board house's minimum widths and minimum spacings, and double them, for a start.