Do you live urban, and how are the regulations for owning poultry in your area? Check into that first of all. You might have a regulation of how many and/or what you can own.
First of all, you should figure out for yourself if you want them for eggs, meat, ornamental or a combination of those. According to your choice research the duck breeds, care and raising well before getting a duck at all. They can live up to 15/16 years so it's a commitment just like a dog (if you don't wanna butcher and the predators do t get it.
Second, be aware of the cost and requirements for all that you need and want. The first month is gonna be the most taxing as they most likely have to stay inside til they grow out some real feathers before you can have them stay outside. It's a full time job as they're messy with their water, poop a LOT and therefore smell accordingly. They can eat like there is no tomorrow in that time too.
But you will instantly fall in love with the little fuzzies, their antiques and personalities. And then you're infected with the duck disease... Lol. Meaning you want more... And more...
As to convincing your family, I'm not quite sure. Do you already have other animals in that belong to other family members? Tell them you want some of your own too (you should at least get 2, as they are flock animals and don't do well alone) and let them know about their good uses, i.e. insect and pest control, good for gardens as fertilizer producer, the free eggs, the fun and relaxation while simply watching them. The list goes on and on. That's all I can tell you IMO.
I know that my BF wanted chickens and told him flat out, if he gets chickens I will get the ducks I always wanted. He did, and so did I and he was not happy! But within a week he fell in love so much that HE decided to expand and breed them. Now we got 65 ducks of 8 different breeds. Lol. Good luck!
