GND in a DC circuit with circuit board
Based on the picture in the question you have a PCB stripboard such as following



So I would layout the components such that all the pin connected to ground use one strip. Also Circuit 1) and Circuit 2) are both the same with respect to GND.

I suggest that you look at fritzing. They have tools that will help you layout the board on CAD before you start soildering. Below are some links that might be of interest to you.

References:


Fritzing Tutorial Stripboard
Fritzing 
How to make traces on an universal PCB?