Building a sample that truly represents the original dataset

I have a set of 750 geographic points and would like to generate a sample that truly represents the original dataset.

Currently I'm just randomly selecting 300 points but I would like to improve my sampling method. - how many random points do I need to select to truly represent the original dataset? Is 300 enough or do I need more/less?
- I would like a way of ensuring that the random points selected cover the whole space. I was thinking of splitting the points into quadrants and sampling from each quadrant but I don't really know how to implement that.

Any help, advice/ references is much appreciated.