If I just grass feed her will she produce that much milk? I heard the production goes down if she is not fed any grain. What is a good Home cow?
Yes, production will drop without grain, however, if her genetics push her to milk beyond the energy she's getting, you'll have problems. Some cows will milk themselves to the bone. If 'good' genetics designed for commercial dairies, you really need to pour the groceries to her. Kind of need to know what you're doing.
What makes a good home cow? Depends on what you want. How much milk do you want or need? Do you want beef, and how much? Do you want to sell anything? Selling raw milk can be illegal.
Jerseys are popular home cows, as they're smaller than Holsteins. But even they can give 6-8 gallons daily, and high production makes more prone to problems like milk fever, mastitis, etc. I prefer a beef/dairy cross. I currently have a Jersey/Lowline angus cross, which I breed to lowline for a beefy calf. I take 1 gallon daily from her milking once in the morning, calf gets the rest. She's a small cow (half the size of Holstein?), easy keeper. Gallon a day is plenty for our family of four.
Yes, you could milk a beef cow if you only need a gallon or two, but I'm guessing she might take more feed to maintain a bigger body, rather than putting it toward milk.