> I get that if I leave my startup today I have 90 days to exercise my options.
The number of days to exercise depends on your contract. The typical number is 45 days. Pinterest's number for employees that have more than 2 years of service is 7 years. This number is not set by law, and can be set to anything the founders/investors agree to.
The 90 day number you are thinking of is the law stating that ISOs become nonincentive options when not exercised after 90 days after termination of employment.
> I get that I'll have to pay the agreed 'strike price'
You pay the "strike price" * "number of options you wish to exercise"
> Would I be paying tax as if I'd made capital gains in the amount of the delta between the strike price and the stock's value today? Would the stock's value today be based on the company's valuation at the most recent round of funding?
Assuming you were awarded ISOs, you do not owe capital gains tax under "regular income tax" upon exercise. You only owe taxes upon sale of your stock that you have attained through exercise, at some future date.
However, depending on your amount of gains, other income, and your effective tax rate, you may owe tax under AMT. Consult a CPA with experience in this. It should be simple for them. (I believe you get some tax credits for this AMT payment when you end up selling your shares in the future)
The company's stock's value is set by the BoD meetings. This may or may not be the same as the previous round of funding.
> If the company goes on to raise more VC funding, would I be liable in future years for the 'capital gains' on this stock?
You are only liable for "capital gains" when you sell the stock.
> If the company went on to fail, would I be entitled to tax breaks for loss of stock?
Good question! I hadn't thought of this one. My guess here would be "yes", you would be able to claim a capital loss equal to the amount of money you paid to acquire your stock.