I think you may find that this is neither as simple, nor as wise, as you may think. ISOs, or Incentive Stock Options, are granted to employees to convince them to work harder, longer, for a lower salary, to take on extra risk, stay with a company for longer, or as a way to reward individuals who have made particular contributions to the company. They typically vest (not the same as "investing", which I saw in another comment) over time so in order to fully realize the benefit you need to stay with the company for a period after grant rather than leaving and taking skills and specialized knowledge with you.
Because you have stated that this is a private firm, the market for the stock is likely very low. In fact, if all of the stock is held by either the company itself (possibly in a lot designated for awarding ISOs) or by private investors, or if the stock is restricted (which means it cannot be sold or transferred), there may be no fair market value simply because there is no market.
In publicly-traded companies, market value is easily determinable from the current market price for the security, which is usually easy to get.
In a case like this, exercise of the ISO would trigger a transfer of unlisted stock (hence, "private") typically from the company itself, who should provide you with the fair market value at purchase or in tax notifications at an appropriate time. But again, unless there is actually a market for the stock, then there would be no market value.
It might even be that your ISOs are for purchase of company stock "after the company has gone public", when a market value can be calculated. If the company has incorporated, it certainly has stock - but as I noted above, that stock could be limited, restricted, or otherwise not as liquid as you may hope.