I know I'm repeating what others have already said, but before you buy eggs you need to get some supplies. Hatching and brooding chickens or ducks requires an indoor brooder, unless you want to wait until after the last frost day so you can get them outside. Even then, you need an incubator, a shelter, heater, feeders and waterers, and bedding for when they're too small to go outdoors. Also you'll need some kind of fencing to keep predators out and probably a covered run, at least for when they're little. Even if you're in a residential area with few predators, baby birds will be easy targets for raccoons, crows, rats, just about anything that eats meat. Adult chickens or ducks may be ok in a fenced in back yard during the day if predator pressure is limited, but they still need a shelter for night time to keep them warm and dry and safe from predators at night. Also you need to have a plan for the males. Eggs don't come pre-sexed. You've got to either eat them or sell them, and realize that they won't sell for much and will likely get eaten. I'm not sure about ducks but you can't have a functional chicken flock with a 1:1 female to male ratio. Chickens should be more like 8:1 or 10:1.
That said, I would strongly advise against getting eggs off ebay. As JaeG said, shipped eggs tend to have very poor hatch rates. I've heard best case scenario is around 50%, and that's if the shipper actually knows what they're doing. Often they all arrive damaged and hatch rate is closer to 0%. There's a lot of people on eBay that don't really care and will sell anything with no guarantees just to get your money. Try to find someone local. I hate facebook but it IS very useful for finding local hatching eggs or birds. Craigslist sometimes has options, too, but really facebook is unfortunately the place to go if you want a lot of local options.
As for chickens vs ducks, I've only had chickens, although I really want to get ducks someday. But I'm waiting until we move to a property with a water source. I would NOT do ducks without a water source, unless you want to be out refilling a kiddie pool with fresh water every day, and hauling water out in winter when the hose line freezes. Also, if you're in a densely populated residential area, your neighbors will likely not appreciate the noise. Just some things to consider.