I'm sure you will get a lot of advice from a lot of different people. Here is my $10 worth of information:
William Yates is a perfect place to start. The designer John Thiess, I believe, envisioned the course for just that, a family atmosphere where you can enjoy the outdoors with kids. I would suggest going down to Disc Golf World with them one Saturday and pick out a simple MID RANGE/ALL ROUND disc. It gives you an opportunity to talk to local golfers and your kids can pick out their fav color. If you don't like the social thing, check out all the great DISC GOLF websites online. As far as first time discs, I prefer and suggest the Innova ROC. It's a great ALL IN ONE disc. And perfect for William Yates. Anyway, what ever you do, have fun.