TLDR
Exercising your ISOs in January will maximize the amount of time before you must pay Alternative Minimum Tax.
When is the best time to exercise ISOs?
Incentive Stock Options (ISOs) are eligible for favored tax treatment, which means they are not subject to withholding tax upon exercise like NSOs. However, they are subject to Alternative Minimum Tax (AMT) if the size of your exercise is beyond the exemption limit. Fortunately, AMT isn't due until you file your tax return the following April. As such, you can maximize the amount of time you get to keep your money by exercising early in the year as opposed to late in the year. However, 409 updates to the Fair Market Value of your stock are often triggered at the end of the year so waiting until January could result in a higher FMV which means higher taxes albeit delayed. If that is a concern, ask company officials about when they plan to do a 409 update since most startups only do them following new rounds of financing.
See this link for more ways to save money on stock options. Feel free to contact the ESO Fund for assistance in funding your stock option exercise while not having to face the financial risk of investing in a startup.