I have a small Farm along with working a full time job. Which version do I use to do my 2016 taxes so that I can record all of my farm expenses and income?

Based on what I see on my screen, you're already using it. Home & Business. Under the business tab you'll report your farm income and expenses in the Farm Income & Expenses section.

When I first logged into TurboTax it said that the Home & Business was now called Self-Employed, which we are not, so wanted to see if this was correct or if I should use another version.

The only difference between Self-Employed and HOme & Business, is the spelling. (Literally!) They just renamed the online version (but not the desktop version) in the expectation it would "reduce confusion".