Dairy cows are slightly different than beef animals.
As far as making $ off them goes, that's not true unless you make your own feed and don't have to buy much. Otherwise you will spend more on grain feeding just to get them to produce.
Jerseys are good cows. They are small, fairly efficient and won't eat as much as a holstein. You can expect (this is a good quality cow on 18-20% protein grain daily) about 4-6 gallons a day, obviously less as she gets milked out and closer to drying up.
You could go with a brown swiss or guernsey, but they are bigger animals and less efficient at converting feed to milk.
Dexters and mini jerseys tend to be popular, but they give much less milk.
Keep in mind that the cow will only continue to produce if you breed her back and calve her in annually. You don't want too many calves on her otherwise you will 1. not have enough extra for your family, or 2. the calves won't get enough to grow and stay healthy.
Figure that each calf will eat 2-4 gallons each per day (depending on the breed and age of the calf). They should have milk for at least 3 months, but if you are raising them for beef you can keep them on her as long as you want (up to 6-9 months, I wouldn't let them any longer) as they will grow better and faster on milk vs milk replacer.
Feel free to PM me if you'd like. I was born and raised on a small dairy farm in Maine and run my parents farm right now. I am currently building a barn and calving in my own herd of Normandes and doing what you are explaining but on a larger scale (15-20 milk cows, calves for replacements and beef, make my own products and keep cows as nurse cows so I don't have to buy milk replacer for calves)