Inflation rate is irrelevant, all you want (ideally) for European options like SPX, RUT, NDX are the actual interest rates being used by the market makers and the actual PVDivs (present-value-of-dividends) for each contract. You can use futures as you are saying for the quarterlies, but using that data to infer other expirations involves ignoring the true PVDivs, which can be quite lumpy so it's essential to do them expiration-wise if you are serious.
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But, accurate rates and PVDivs turn out to be secondary for European options ... your target is really the forwards, and you can get accurate forwards using rather poor interest rates (like Libor) and with no assumptions about, or knowledge of, dividends. Good forwards are 90% of the problem, after that you can worry about improving your interest rates for the discount factors if you want to.
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For American options, accurate interest rates are more important as they are key to the early exercise boundary determination.? ?
