Three stories? Depending on house construction and device layout, that could be difficult to get full coverage.
Well, since you want N support, you'll obviously want a router with that, but another factor to consider is 2.4 Ghz versus 5 Ghz. You can find a router that supports only one, only one at a time or one that supports both a the same time. usually they're known as dual-band routers.
I would suggest getting something locally since it'll be easier to return if you have problems with it. And you may with your house. If you're comfortable running ethernet wire to the rooms, that may be an easier solution, especially if you want to set up multiple wireless routers. While they can be configured to bridge with each other (especially if you use a custom firmware like Tomato or DDWRT), it's usually easier and more reliable with a wired connection.