For Jiko's private Wine Room, the minimums are $2,500 for half of it and $4,000 for all of it.
To use the entire restaurant while it is closed (i.e., for brunch or lunch, ending by 3:30pm) the minimum is $1,500, but the meal will be catered by Disney Catering & Convention Services and not cooked by the Jiko kitchen (if that makes a difference - you can prolly ask for the same dishes, they just won't be executed by Jiko's chefs).
A bride was recently quoted an $800 minimum for a buffet lunch at Yachtsman Steakhouse before it opens for business - just know that you may be quoted something different depending on the day of the week, time of day, etc.