choosing a distributor

Because embedded systems require very tight memory and hardware requirements you will not find a distribution that will just work on your hardware. You will need to perform some research and development to build a specialized Linux kernel and your required software to fit the specific architecture and hardware needs.

Checkout the yocto project as GoingEasy9 recommended, they are working on scripts that will simplify building a custom Linux based operating system for embedded systems. The only way you can make it easier on yourself would be if you hire a developer to do the work for you.

All comments reported here are valid and useful but I'd like to add my opinion as well.
You've opted (or you're opting) for XILINX, maybe because you're interested in a Field Programmable Gate Array devices, I don't know what kind of field you're going to cover with your embedded solution but before taking a decision it could be useful to understand what kind of product you're trying to do.
First of all take a look at hardware specs and what's available in your reference target market, choose two/three hw platforms and then concentrate on the OS later on. Linux is a common choice nowadays but it's not the only one, it's obviously my favorite when it's possible (like Woboyle with his ARM boards), sometimes other solutions are preferred. Sometimes VxWorks is better than Linux, sometimes it's not, someone argues about better performances for Windows CE but I don't want to go on with it, I don't like it and I don't wanna start a flame war.
I've worked with SoC (System on a Chip) devices on BGA packages and I've used Axis devices (ETRAX in my case), they're excellent for particular applications (media stream handling), maybe they suck if I use them for heavy disk I/O operations where an ARM device (or an Atom) may perform better. I've never worked with a Gate Array or with VHDL stuff (even if it's a cool thing where I'd like to invest more time), but xilinx it's an important player in that particular field.
Just to be sure take an overall decision on what kind of hardware you may use, then take a look at various manufacturers, they certainly have some sort of Linux port.
You may find "mainstream embedded linux ports" on general purpose devices but if you're "going deep" with particular hardware (telco motherboards, metro fibre hubs, two way radio systems, ...) it's quite common to have a customized linux distro. I'll definitively stay with mainstream distro (Debian, OpenWRT, Android ?, Yocto ?) when possible but sometimes you cannot use them.