An average shiny new penny from the supermarket is MS-63. A really pretty one with no easily visible marks is MS-65. If you are exceptionally lucky, one will be MS-66. Distinguishing the difference between these uncirculated grades is where most of the black magic in coin grading is. Even with years of experience, coin dealers will disagree about these grades.
Some coins are very difficult case studies.
European coin collectors think that this American system of grading uncirculated coins is just downright crazy. As a novice, you probably won't be able to tell the difference between AU and Unc coins. I know I have trouble a lot of the time. The most important thing in grading an AU coin is to know is where the high points are on a particular coin so that you can look for the minimal wear there. Practice by taking a new coin from the bank, rub it back and forth on your mouse pad vigorously a few times, and see if you can see the wear.