SRIDs are used as a means to distinguish between the many different coordinate systems. Often there are several coordinate systems that will be suitable for the task you are trying to achieve.
The first decision you need to make is whether to use a geographic (latitude/longitude) coordinate system or a projected (x/y) coordinate system. If you are working with areas, distances, directions, or shape and want to carry out any spatial analysis you will want to use a projected coordinate system. To highlight this, consider a geographic coordinate system using degrees as units - what is area measured in? Degrees squared? Which is nonsense really - you must have a projected coordinate system in, for example, metres.
Next you will want to further consider which property is most important to your task, as you will have to choose a projected coordinate system which preserves it.
- Conformal projections preserve shape;
- Equal Area projections preserve area;
- Equidistant projections preserve distance;
- Azimuthal (or True-Direction) projections preserve direction.
There are some projections that preserve several of these properties, though some accuracy is sacrificed as a result.
A further consideration is the scale at which you are working - is it global, national, or regional? Some coordinate systems will be accurate for a specific area only, others will be accurate for a larger area.
The topic of which specific coordinate systems to use under which circumstances is a very broad one but hopefully this will help you understand some of the considerations to make when deciding.
For further reading, the following link discusses projections and coordinate systems in much more detail: