From what I understand there isn't a minimum (but I could be wrong... if anyone knows 100% please share in the comments below). That being said here is a helpful tool to help you better understand the passive income potential from your NEO holdings
With a lot of these passive income coins/tokens it is important to get as many of them as you can at the lowest possible price early on as that is the best way to get the most % passive ROI for your overall investment.
Example:
50 NEO @ $5 each = $250 investment = 5.3924 GAS per year = ~$86USD/year in passive income (at today's prices)
VS
5 NEO @ $50 each = $250 investment = .5392 GAS per year = ~$8.60USD/year in passive income (at today's prices)
Basically the price rise on the NEO token itself is = to the price rise of your potential annual passive income by staking it (so again getting in as early as possible not only pays off as the token rises in value since you COULD sell them at any time, but also allows you get to multiple times more tokens which in turn provides multiples on your long term passive ROI potential). This same concept is true for all of these different passive income coins.
Sidenote: In NEOs case there will only ever be a finite amount of NEOGAS produced so its price will almost certainly rise over time, meaning the above numbers are the low-ball passive ROI values (based on todays NEOGAS price which is currently $15.91USD).