The price for each share of common stock in the offering and the related warrant will be at the Initial Price (as defined below), which shall be paid in cash.
You are awarded units based on the number of shares that you own. So 1000 shares owned give you rights to 1000 units. You then get to buy 300 shares at the offering price. It specifically states that the offering price is for the shares you are purchasing. Not the units.
Further by way of example, if the Initial Price ($5.50) is lower than the Alternate Price, then the stockholder choosing to buy the 1000 units will pay the sum of $1,650 ($5.50 x 1000 x 0.30).