It’s horses for courses, Anke.
There are more than 20 adults here and more than 10 children. It would take a lot of goats, and those goats would take a lot of looking after, to meet our needs!
With a small closed herd primarily for home consumption, and careful sourcing of the original stock, Johnnes shouldn’t be an issue. The benefits of running sheep plus cattle is a grazing rotation => efficient use of grassland, healthy pasture and reduced worming. If you don’t have grassland, then - assuming you’ve got scrub and or hedgerow or something, of course - you’d probably be looking at goats.
Setting up for milking and washing down is pretty much the same whichever species you are milking. Cows have four teats which you milk 2 then 2. Goats have 2 teats so you have to wash down, swap animals and wash another twice as many times

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Personally I’d find it easier to milk one or two cows than five or six goats to get the same amount of milk! Lol. We can flex our milk somewhat depending on whether the cow has a calf at the mo, which field she’s on and how much grass is in it, whether we separated the calf overnight or not, etc. If we don’t want as much milk we leave the calves with the cows and just milk the Jersey; if we want max milk then the cows go on the best grass, the calves off overnight, and so on.
Our cows are hand-milked once a day. For some of the year we don’t need to actually milk the crossbred, her calf keeps her happy and we get enough from the Jersey.
We could get 30-50% more milk if we milked twice a day, but at present we don’t need to push them. Early on in the Jersey’s lactation, when the calf isn’t taking so much, we might milk her twice a day to keep her comfortable - but we don’t usually need to do that for more for a week or so.
We eat 1-2 bullocks a year, so we don’t in fact sell much beef, or indeed any most years. We sometimes sell a few halves of lamb or hogget. But yes, a small family would probably need to sell some of the meat, and or do swapsies with neighbouring farmers / smallholders. You could of course use a less beefy type of bull than we do and manage the meat production down that way - a pure Jersey bullock at 9-10 months old would probably give about half the amount of beef that the 3/4 beef bullock did. You could send them off younger if you wanted less still.
Another alternative would be to produce animals like Luther, and sell the surplus meat you don’t want to the butcher. (Our butcher was extremely complimentary about this bullock.). No hassle at all

I’m very happy to eat goat meat, but I can’t imagine ever pronouncing it better than this wonderful rose veal beef we produce.

Tastes differ of course

Finally, one thing which is very individual and is pretty important is which animals float your boat. If you don’t much care for cattle but love goats, then you’d do it with goats! The OP is clearly a lover of cows, so whilst it’s great to explain how goats compare so s/he can make an informed choice, it sounds like the OP’s heart is with a Jersey

(Of course, if s/he’s only got 3 acres, and doesn’t want to or can’t rent some more, then it’s probably going to have to be goats anyway.)