I am new to TeamCity and currently installing it.
It was asking whether I want to be running the server under a "user account" or "the SYSTEM account" / running the agent under a "user account" or "the SYSTEM account".
I assumed that since my version control (clearcase) is configured to my employee id, I should select user account.
Is my assumption correct? When should either the SYSTEM account or a user account be used? What is the difference between them?
What you're talking about is allowing TeamCity to run as LocalSystem vs a specified user account (local or in ActiveDirectory). LocalSystem is highly priveleged (see this article).
If you are interested in following the principle of least privelege, you should create a user account. If you're running TeamCity on your local workstation, LocalSystem is probably ok.
The same advice applies to the build agent.