I would like to know what makes a good stock market index and the factors affecting the structure of the index?
Broad, accurate, and diversified scope for investing purposes. although the definition of "good" is subjective.
In the big picture (not for investing purposes) an index is suppose to accurately represent "something." If it does, then it is doing its job and is "good."
In the case of investing, you must first ask what is your purpose. If you are trying to represent the US stock market, for example, you want something that is accurate in a meaningful way. The S&P 500 accurately represents "the US stock market" in terms of dollar value. Unlike the DOW, it captures the lions share of the dollar value of the US market on any given day.
On the other hand, if you want to measure "all" or the US market (not just the biggest piece) you will need to use something like the Russell 3000 (98% of the investable market).