The Jersey cow is one of the more popular house cows. The Jersey is smaller than most other breeds of cattle and seem to have better temperaments than others as well.
I brought a young jersey at the same time l brought a young freisen cow. I had to hand feed (bucket/teats) for a while as they were very young when l brought them.
As they were both hand raised they were quite friendly and happy to stand for you when you walked towards them, but l did find that the jersey cow remained friendly while the fresian became a bit more stand-off ish as they got older.
I also worked on a dairy farm for a while, the farm milked about 300 cows which were mosty Fresian cows but there was about 12 - 13 jersey cows mixed in with the herd.
The reason many farmers will milk a percentage of jersey cows is because the jersey produces a higher concentrate of butter fat in the milk which helps boost the price paid for the milk by the milk factory.
On the downside, while the jersey produces a higher butter fat ratio than most other cows, they do produce a lower volume of milk in total.
While working on the dairy farm l found that most cows were fairly quiet and easy to milk, but there was a number of Fresians which did play up and let go with a kick when putting on the milk cups or removing them, but l never came across a jersey cow that would attempt to kick me.
I guess all cows have a potential to be great house cows and all cows have the ability to kick, but in my experience the Jersey cow is better suited than any other breed for people who want a pet cow which they can milk themselves or simply keep as a pet and possibly breed with.