would like minimal color with a vintage look and feel 
i love the idea of a vintage typeface logo (see what you can do, i'm not stuck on this i just like it)
to me the main emphasis in the name should be on the word livestock, not family farm
ideally it will have a one color version
do not include barn or machinery!
i would prefer a focus on grass and animal husbandry aspects
animals are optional, if used:
appropriate animals would be sheep and pigs, to a lesser extent cattle, goats and poultry (waterfowl included)
currently using these colors, just to give you an idea you don't have to stick with them for the logo:
94c973-a minty green
2f5233- a darker almost forest green
b1d8b7-a blue green
76b947-lime (rarely used)

Family Farm Livestock