You need to understand that the difference between the "par value" that you paid and the actual (fair market) value is an income to you, and you'll have to report it and be taxed on it. Different countries manage it differently, in the US once the restriction is lifted (i.e.: the restricted stock becomes vested), you have to report gain (which is not capital gain) on the difference between what you've paid (0.001 per stock) and what its really worth on the day of vesting.
For many startup investors that invested in the early stages that difference may be extremely significant. When investing at startups, or restricted shares that you expect to appreciate significantly, make sure to talk to the tax adviser before investing, to learn what to do and how to avoid the huge tax bill you may end up getting when it vests.
You can pay for restricted stocks whatever, doesn't really matter. Most people don't pay anything at all. Why? Because its only yours when it vests, and its then when you also pay taxes on the difference between the price paid (if at all) and the real value of the property received. Unless you had a good tax adviser to mitigate that, which apparently you hadn't if you're asking the question.
How the "fair market value" is determined? This is called valuation and is done by independent accountants.