Hey Theresa, I am in Orange Park and in the same boat as you. I have been to a farm in Starke, Cognito Farm, that raises cattle, swine, and chickens, but I have not purchased from them yet. I did the tour of their farm and was really impressed, but I do not have the freezer space to make a major purchase yet (which is what I eventually want to do).
I know you're looking for something more specific, but check out http://slowfoodfirstcoast.com/farms.html for some places that are local for us.
Good luck to you! 8)