A lot depends on what you want to do with Linux in 2013. Not being a smart-@$$ here, but your requirements for audio recording and video editing are going to be a little different from those for surfing the 'net and reading email, just to make an example.
You asked about integrated CPU/graphics? Looking at your example it appears you're not asking about graphics on the motherboard, but from within the CPU? I'd not be too prone to do that - a chip that tries to do both might not really do either too well, but I have yet to experience such a beastie, so take that with a small Siberian salt mine in your hip pocket. (For all I know, there may be hardware synergies that result in improved performance if you can get it supported in Linux... research will be key for you in this decision.)
Also, it looks like you are maybe wanting to jack up your case and drive a new motherboard under it, and that you like AMD's processors. You're not alone - lots of folks like AMD. That said, for raw performance and reliability, intel's Xeon processors are just rock solid. (Expensive, they are, but you get what you pay for.)
As for motherboards, there are a lot of personal preferences out there. I like MSI, Gigabyte, and Asus boards, as these are generally well supported by Linux and high quality products. I've had some bad experiences with Asrock in the past - customers brought me machines they bought from another builder which basically fizzled out after three months of run time. Build quality was decent, but the motherboards were useless - fried capacitors, other component damage - this with Antec power supplies (which are actually pretty decent). Since then, I've been really leery of anything made by them.
A good place to do research is http://hardware4linux.info/
. Use their search functions to find out what they know about hardware you're considering using.
If you're looking for pre-built, the nice folks at LinPC.us
put together some nice systems with PCLinuxOS pre-installed. I bought one for my wife a few years back, and it's been a top quality unit - still running as I write here. Eric, the fellow who runs LinPC, favors less powerful gear, but he's trying to build more affordable systems. That said, everything he builds is first quality.
I ddidn't mean to write a book here, so let's wrap up. There's good stuff out there - figure out what you want to do and build to your needs. One last thing: the example system that Old-Polack lists has served him pretty well so far by all accounts, and it looks like he got the pieces parts from Newegg.com - you might take a look there and see. They have a very nice feedback system that can help you sort the wheat from the chaff here.
Good luck with your enterprise, and may your CPU never overheat.