I'd recommend Debian-based Ubuntu, but you should really pick up a distribution based on your own thoughts, not somebody else's.
Hardware question is difficult to answer..there are a lot of hardware parts that do work under Linux (read: that already have working, native drivers in the kernel), and more coming all the time. The LinuxQuestions HCL (check the link at the top) helps you decide, but primarily you should pick up the parts either based on their price or quality/what you need. Price because there is no reason to pay too much, and quality/needs because the computer is your tool, not just something you decided to buy with blind eyes. After those selections you usually have several options, from which you can decide based on price and hardware compatibility (refer to HCL and search the web).
Nowadays pretty much any pc in the store does the job. Linux kernel has driver support for a lot of hardware, the most usual ones work just as certainly as they work on Windows (or even better), and even for those that are "difficult" there are usually easy solutions. Ubuntu is a good example here; it's Restricted Drivers Manager app lets you just click some checkboxes and have it fetch what is needed to get some of the hardware work that needs proprietary drivers: nVidia and ATI graphics cards, (for example Broadcom) wireless cards that don't have native Linux drivers that would work without parts of Windows drivers etc. Some people say that Broadcom43xx chips should be avoided because they're impossibly difficult to get working under Linux; that's crap, on Ubuntu you need two clicks to get it work. Even manually it's a matter of few simple steps.
So..read some ads or visit local stores, pick up a few pc offers that look appealing to you (pay attention to the amount of RAM, cpu frequency, grahpics cards or whatever is important to you) and collect their specification lists. Go back home, get a cup of your favourite beverage, visit LQ's HCL and/or do a web search to find out if the hardware is known to work without trouble under Linux. Most of it should. The troublematic parts are usually graphics cards (they usually work, but getting 3d accelaration at full speed means the manufacturer must have drivers for Linux - ATI and nVidia do, at least for the newish cards), webcams and maybe some not-so-standard products. Not sure how Microsoft wireless magic keyboards work
The last good advice I can give you is to fetch and burn a Linux live-cd distribution, and ask from the store if it's possible to test it with the pc you're intending to buy. Live-cd distribution doesn't need to be installed and it doesn't "interfere" with the machine, so it won't break anything - but you get to know if it boots, if sound and video works (note: not all codecs might be there on the live-cd disc, but test with the common formats if you can) and so on. Ubuntu Desktop disc is a good one - it's a live-cd, you can later use it to install the thing, it should detect most hardware easily, and if there are some that require proprietary drivers or such, it should tell you that too (with other live distributions those hardware parts might not work at all, so they would seem like they don't work to you, even if they did with the right drivers installed after the initial setup).
That's about it..don't think it's so difficult to find hardware that Linux likes to run on. Maybe it used to be, but not anymore.