Family minimalism is a lot harder I think than individual minimalism. Most minimalist blogs paint a picture of a single male hipster with a macbook couch-surfing between RoR consulting gigs. Family minimalism cannot be that extreme.
Our books and cds were the easiest to get rid of, we both have kindles, and noticed that we never re-read books anyway, and listened to mp3s or streaming radio rather than cds. The hardest bit was thinking about what it represents in financial terms.
I would say keep the musical instruments. A couple of ideas I have seen floating around are the 100 things idea, where each person has 100 things, and if you want to buy something and have 100 things you have to decide what to ditch. I think it is fully acceptable to have a musical instrument as one of your 100 things.
The other idea I like is splitting things into the create or consume categories, and feel better about holding onto things that let you create. Anything related to consumption like a TV for example should be on "consider ditching" list.
As far as cooking goes, well if that is your thing keep it. We ditched ours as we ate too much anyway. We worried that we would spend more money and eat out more, but basically we ended up eating less and losing weight.
For us it has meant outsourcing a lot of stuff. Instead of burning all home movies and photos to blu-ray, we are more selective, and upload stuff to the cloud. We used to have external hard drives and actual servers, now it is just laptops and the cloud.
Overall we are spending about the same. What we save on collecting crap, we spend on services. We are saving on power, and go out more. We spend less time at home, and less time cleaning up.
EDIT: Plus now we only need a much cheaper and smaller flat. Rent is cheaper, but heating is MUCH cheaper.