100 points is a good starting point, but understand you'll be limited in what you're able to do with it. As you mature into your DVC ownership, you'll probably find yourself getting Addonitis -- the DVC disease that makes you want to buy more points.
Do you have any qualms about pulling your kids out of school for your trips? Bookings require fewer points if you travel during less popular times. These mostly exclude dates when kids are on school vacations (summer, spring break, Christmas). If you can travel in September or January, for example, your points will stretch a lot farther than they will at Spring Break or Christmas. The DVC calendar is broken into five seasons: Adventure, Choice, Dream, Magic, and Premier. (They're alphabetical, with the points increasing as you move down the list. The more popular the time of year, the more points it will cost to stay on a date in that season.) Each day of the year is assigned a season. For example, a week in a studio at Saratoga Springs Resort is 95 points in the Adventure season. A week in the same room is 159 points during the Premier season.
The size of the room you stay in also makes a difference in how many points you need. DVC resorts (mostly) have studios (sleep 4 in one room - similar to a hotel room), one-bedrooms (sleep 4 or 5 depending on resort - full kitchen, common area with a fold-out couch, and one bedroom), two-bedrooms (sleep 8 or 9 depending on resort -- same features as the one-bedroom, but with an extra bedroom), or a three-bedroom grand villa (sleeps 12 - a giant villa!). Again, looking at Saratoga Springs Resort, I already indicated a studio in Adventure season is 95 points. A one-bedroom in Adventure season is 183 points. The two-bedroom is 246 points, and the grand villa is 501 points. Banking and borrowing your 100 points, you'd roughly be able to do a week in a studio every year, in a one-bedroom every other year, or in a two-bedroom every three years.
The age of your kids will also play into the room size choice. As your kids start to grow, you'll probably want to have your own bedroom. If they're smaller, it's not such a big deal to have them in a studio with you. (You'll also probably find out that when the kids start to get older, there will start to be discussions about who "has" to sleep on the fold-out couch. When they're young, the discussion with be who "gets" to sleep on the fold-out.)
Some resorts also have different views, which have different point values. For example, Animal Kingdom Villas has studios with four different views: value, standard, savanna, and concierge. In the adventure season, the points for a week would be 69, 81, 102, and 125, respectively for these four views. The nicer the view, the more the points.
Weekdays and weekends also have different point costs. It costs more to stay on a Friday or Saturday night than it does to stay Sunday through Thursday nights. Taking a 6-day trip to eliminate one of those weekend nights can save you some points. A nice feature of DVC is that you're not set to a specific number of days. You can book a trip for a single day, if you like. (Some timeshares are based on 7-night stays only.) The difference between weekday and weekend nights used to be more profound before DVC made some adjustments to the
point charts a few years ago, but they still exist to some extent. Using the same example from above, a week in a studio at Saratoga Springs in Premier season was 159 points. That's five weekday nights at 21 points a night, and two weekend nights at 27 points a night.
Spend some time looking at the point charts -- you can find a link to them at the top of this forum. Look at different resorts, seasons, and room sizes to plan out how you want to use your points.
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