Hi Stella,
Wow you're so lucky to be able to spend 3 weeks in Disney World, you'll have so much fun!
I think there are several things you need to weigh up with regard to purchasing the Disney Dining Plan. Firstly there are 3 types of plan, there is the Deluxe Plan, details
HERE, regular plan
HERE and the new Quick Service plan
HERE. As you can see they differ quite a lot in both price and what is included. I personally would visit the menu pages on allears.net, roughly decide which restaurants I would want to eat at and price up my meals for each day to see if it is worth it for me to buy the plan. You need to ask yourself will you really want to eat a sit down meal everyday for 3 weeks? If the answer is yes then the regular DDP can save you lots of money as you also get a counter service (think fast food) and a snack every day too.
I've used the DDP several times and it really is nice to know that all your food is already paid for, I also love planning which restaurants we will visit whilst my girls love to spend the snack credits on ice-creams, funnel cakes and candy!
Have a great trip and feel free to come back and ask some more questions,
Jo