Acquisitions can be structured differently, but the ones I've worked through most are structured so the new company stock you received retains the characteristics of your original grants/stock.
I.e. if you hold old company stock, your cost basis and holding period carry over, and if the stock is from exercised ISOs, the "2-years-from-grant" qualifying disposition requirement should carry over as well even if it's a replacement grant from the new company. You should be taxed on that stock when you sell, and not because of the acquisition. In your case, it sounds like it will be a long-term capital gain.
Owned shares that are paid out in cash are taxed as short-term or long-term capital gains based on the holding period of the original shares (in your case, it sounds like long-term gain).
Unexercised options that are paid out in cash are taxed as ordinary income.
Unvested options and RSUs usually (but the terms of the acquisition will dictate this) become an option or RSU grant at the new company.
The acquisition has to be structured in a certain way for all of this to be true. I've never seen it, but know it's possible for an acquisition to be structured in a way where gains are realized on the acquisition date instead of the day you actually sell the acquiring company's stock.