I like to browse around for my first few days and get ideas, then I shop toward the end of my trip. If you have a Disney Visa card you can get a discount at the World Of Disney store in Downtown Disney. Also, they have a huge selection of stuff at Downtown Disney with many different shops for all different tastes. It is a good place for one stop shopping!
I would plan on around $300-$500 depending on your taste. Another idea is to set an amount you want to spend for each person and then find something in that range. There is so much to choose from, I am sure you could find something for anyone in just about any price range.
http://disneyshopping.go.com
My suggestion is to either have the things sent to your room (if possible) or shop at the end of the day. Otherwise you will end up lugging around everything all day and that gets tiring! Every resort/onsite hotel I have ever stayed in had an excellent gift shop as well with disney merch.
Good Luck! And happy shopping! =)
The best place to shop is World of Disney in Downtown Disney. Unless you are looking for more park specific items, WOD will give you a large selection.