Where do I enter office equipment expenses and other expenses associated with being self employeed. Under Income and Expenses or Deductions and credits?

Neither. Anything and everything, including home office stuff is entered on the SCH C. In TurboTax, all self-employed business stuff is dealt with in the Business Income section. Where that section is, depends on what version of the program you are using.

In TurboTax Self-Employed (online) and Home & Business (desktop) all business stuff is dealt with under the Business tab in the section titled Business Income & Expenses (SCH C)

For all other versions it's dealt with under the Personal Income (or Wages & Income) in the Business Income & Expenses (SCH C) section under the Business Items heading.

If you are using the online version, then you *must* use TurboTax Self-Employed since you are claiming business expenses.

If you are using the desktop version then you *must* use Premier or higher since you are claiming business expenses.

Carl,  I think you can use any Desktop version.  I never heard it has to be at least Premier.