There is also a special scenario in the event of a buyout, where all options immediately vest.
Actually, what usually happens is that the options are compensated as cash *in lieu of* equity. I.e. the acquiring company will write you a check equal to the per-share exit valuation of the company minus your strike price. Unfortunately the IRS treats this as ordinary income for option holders so you pay the maximal tax rate. That is, unless the employee took a risk and exercised while the company was still private - which you can do if you have the means, as soon as your options start to vest. If you do that at least 1 year before the buyout then you get the much lower long-term capital gains rate.
If I were working for a startup I would try to get fully vested shares (a "grant" of common shares). Or options with perhaps shorter vesting period so you can buy them out of your own compensation.
As a contractor you probably have no visibility of how the company is capitalized. Ask to see the "cap table" but they probably won't share it with you. You at least need to know how many shares are outstanding, and the valuation at the last fund raising to be able to decide if the equity is a good investment or if you should just push for more cash and invest it elsewhere. Try to guess how much money the company will need to raise in the future so you can figure out how much your share is going to be diluted by then. My guess is if the company is already up and running and able to pay you market wages, you're probably past the window of opportunity to make big bucks on options.