This all depends on so many factors.
Under the current tax system, ISO shares receive special tax treatment if you sell at least two years after the stock grant and one year after exercising. Furthermore if you expect the value of the shares to increase over time, exercising sooner rather than later will reduce the amount that gets taxed for the AMT purposes before you even sell anything. If the AMT goes away next year, that latter point will become less of a consideration.
However taxes should not necessarily be your primary consideration. How liquid are these shares? Do you have any idea when you might be able to sell them? Do you have strong reason to believe that the company will ever get to an IPO? Exercising pre-IPO options can be a big gamble. I had pretty good luck with it with the company I worked for, but I've seen examples of companies that everyone thought would go public within a year, and five years later they still hadn't. And of course there's always the possibility that the company goes bankrupt and your shares become completely worthless.
You need to take a long, hard look at your company, how likely you think each of these scenarios is, and make a decision according to those probabilities and your own risk tolerance. Worst case, you exercise all the shares (putting 6% of your net worth into them), and the company goes bankrupt. Probably wouldn't feel great, but wouldn't be the end of the world either.
I don't think that a so-called "cashless exercise" ever makes much sense. That transaction essentially involves selling a fraction of the shares immediately in order to pay for the rest, which you would keep. If you think the shares are a screaming deal and you want to hold them a year for maximum benefit, then put up your own cash to buy and hold the whole lot. If you want to drop the shares like a hot potato and reinvest in index funds, do that. Don't keep whatever fraction could be exercised cashlessly.