We are not going into the intricacies of fly selection on the waterside just yet but suffice to say that the important factors are, in order of importance, size, shape then colour. So when choosing your first set of flies choose a few basic patterns (shapes) and make sure you get several in a range of sizes - 3 sizes is a good start.
Don't get just one of each - no good if you lose THE fly that is working. I recommend you get at least three in each size.
For patterns and sizes check the advice section for the type of fishing you are planning to do. Three or four basic patterns will cover most situations you are likely to encounter.
So you will want three flies in each of three sizes in at least three basic patterns - 27 flies all together.