You've gotten some good info. I will add that different days of the week and different months have lower minimums. If you are trying to stick to a 10k minimum or 15 k minimum, be sure that you select a time of year that will allow that. I am looking at a Sat. in November and the minimum is 25k.
Another idea, I considered, but ultimately decided against, is to have a wedding at a Downtown Disney hotel or at the Swan or Dolphin. You could still do a "Grand Gathering" or a dessert party (not in bridal wear) but the wedding itself would be cheaper. There's an outdoor area at the S/D and several convention rooms. It's not the same as a Disney Wedding, but for some it might be the right option.