Type of shares are generally split into two: common/ordinary (depending on the jurisdiction) and preferred. The former are granted to founders and employees (most commonly as options with a right to purchase common/ordinary shares). The latter are generally issued to investors and include special rights such as liquidation preference, anti-dilution protection, etc. Preferred shares reflect the fact that the holder (investor) has paid a premium in consideration for issuance of such shares. Don't forget to consult with a lawyer.
Typically for founders and employees you assign options that vest (an option to buy a common share at a given price).
The basics of venture math is described by Brad Feld:
The preferences that an investor can put in deal structures change. See http://www.feld.com/wp/archives/2004/07/liquidation-preferences.html
You should talk to a lawyer that has experience with share holder agreements, employee stock option plans and the tax implications of the different decisions based on your jurisdiction.