Welcome to these forums
Your question is much more difficult than you might think (or at least the answer is much more complex). The cost for set up depends primarily on how much comfort you want, and how spartan the equipment
level. 3 young children
will also have a major impact - for example you might be content with a single cabin
with three bunks for all the kids
, or want individual cabins for each (very dependent on age) as they get into middle to later teens, kids
need more individual space, plus each needs more study space, so things can get more expensive.
Intended liveaboard/cruise plans will also have a big impact, plus how capable are you at repairs
. If you are not very handy, but want to do long distance, then a new boat has attractions due to warranty plus reduced risk of problems.
The type of boat will also have an impact on cost - cats are more expensive to buy, but have more space for the family
, and are nicer to liveaboard
Costs for liveaboard
vary significantly again due to lifestyle choices. If you intend to swing around an anchor
rather than use a marina, and catch your own meal from the sea, rather than use a restaurant, life will be much cheaper, but your kids might not be so happy!