The former, the number of contracts in one specific position.
The exchanges have position limits that are meant to prevent one party from having too much influence on the market. But you probably won't come anywhere near those limits.
One popular rule of thumb is that you should not have more than one percent of your captial at risk on any single position. But that rule is really just an arbitrary benchmark that serves as a starting point for the conversation. How much you put at risk is a complex question that involves the size of your account, your trading objectives, and your tolerance for risk.
I often hold multiple positions--across multiple expirations--in options on underlying products like SPY, SPX, and DIA, and those are all very closely correlated. So measuring my risk in an individual position doesn't tell me much. I have to look at how much risk I have on each underlying, or in each sector of the market, etc.
And there are many different ways to measure risk, depending on what kind of positions you are trading. I sometimes take a long stock position and write a covered call, as a swing trade that I expect to close at or before expiration. Mathematically, there is a risk that I could lose the entire cost of the stock, because it could go to zero. But I'm not trading penny stocks, and in most cases, the probability of a total loss is extremely low.
Many people who sell naked calls use some sort of model, based on volatility, to estimate their risk, i.e., their maximum potential loss, because in a raw mathematics, the potential loss is infinite. And that is not particularly useful information, because it's not a real number.
Infinity is not a number. It is an abstract concept.
