In selecting the index and contract month one should consider the following points.
Expiration date: If the investor has a month or two’s view about the market then he should choose that index futures which has a similar time left for expiry.
Liquidity: The index and the contract month, which is the most liquid must be used. This will save cost because of the low bid-ask spread. This also saves hedging costs.
Stock should be correlated to the index: The stock to be hedged should have a correlation with the index selected.
Potential mispricing: One should sell index futures contract which is overpriced. In such an event one can not only hedge but also earn some profit in selling high.
In a nutshell, one should hedge by using the most popular and fairly priced index and delivery month should not be very far since liquidity and predictability of very few contracts are low.