I'm gonna build a desktop but I'm completely and utterly behind on computer hardware. Any recommendations on what specs to get? What video card you recommend? Anything at all?

I don't play games much anymore but I want something relatively capable so I can play new games but not necessarily on highest settings. Let's say a medium-high end computer?

I'm thinking something along the lines of
intel i7 3.5 Ghz quad core
12 gb ram
60 GB boot SSD
2 TB data HDD
??? video card (no idea)
BD-R
600W PSU

But I'm shooting in the dark here so help me out! :)

Well I recently posted what I upgraded my PC with in positive events..

I'm quite happy with the Intel i7 2600K 3.4 Ghz that I got. Wasn't that expensive considering it's speed and overclocking potential. (Clocking it up to 4Ghz seems to be very common). But I don't have the heat sink cranking it up yet. As for ram, I couldn't find a better deal than these (http://www.newegg.com/Product/Product.aspx?Item=N82E16820233143). 4gb per stick :)
I'm not sure about graphics cards either. I got a ATI Radeon HD 5770, but that was last winter. Seemed like the best choice then, but I'm sure things have changed since. Decide on a price range and lurk hardware forums ;)
A good idea is to compare benchmarks on new cards, and your current one, and then google each candidate to see if their something to look out for.

I want to get an SSD too. But I'm not sure if I should wait until the average capacity increases a bit, seeing as how games easily take 10 gigs now. A SSD will probably be my next buy, if not a proper CPU heat sink like the Antec KÜHLER H20 620.

Since you're not planning on playing games, I highly recommend that you get a passively cooled graphics card, i.e. one that only has a heatsink (even if that means that the heatsink occupies a second slot on the mainboard).
Additionally, get a good CPU cooler. Something like the Arctic Cooling Freezer series (http://www.arctic.ac/en/p/cooling/cpu.html) with ridiculously large heatsinks and heatpipes and 120 mm fans.

Also, only use 120 mm fans for your case too and get a large case, where you can properly place the fans to create a nice airflow from the front to the back, past the passive GPU heatsink and right through the ridiculously large CPU cooler (make sure the CPU fan also blows in the same direction).

You will be astounded how silent your machine will be. At night, I can hear my own breathing, even under full load.
The loudest noise now is my HDD, but if you also go for a SSD, you can even reduce that.

Edit:
You could also buy a regular graphics card and replace the cooler with something better. I just saw that Arctic Cooling also has ones with 92 mm fans (http://www.arctic.ac/en/p/cooling/vga.html).
That way you'd have the full power of a regular GPU, but still be silent.