I have been vaguely contemplating my first build for some time, but this has become more urgent because a) my pre-ordered Windows 7 is only a couple of weeks away and b) my aging Athlon 64's mobo has died and I am reduced to using my netbook

Because of the industrial whirring, whooshing noise which emanated from the above dead PC, and seduced by the shiny stuff on SPCR, I want to go down the quiet-as-possible-with-minimum-effort route. My thoughts thus far have led me to:

CPU - Core i5 750

Mobo - Gigabyte GA-P55M-UD2 - cheapest LGA1156 board I could find, seems to offer everything I need and being microATX will fit in the...

Case - Antec Mini P180 - I like the understated styling of the P18x range and this is currently available for quite a bit less than the P183 and has enough space for everything I need.

GPU - Sapphire HD 4670 Ultimate Edition - small, capable, low power consumption particularly when idle, passively cooled.

Heatsink - Xigmatek HDT-S1283 - because SPCR rate it

My immediate concern as a newbie is whether the CPU cooler and the graphics card will foul each other on the small form factor mobo. As you can see from this image:
the GPU cooler extends a little above and behind the card and on the mobo the upper PCIe slot appears to be closer to the CPU socket than on a standard size board:

So my question is will this cause a problem and if so are there any obvious solutions?

That won't work with the HDT oriented vertically (ie. with the airflow front-to-back). It will probably work with the HDT oriented horizontally, with the fan mounted on top.

Disclaimer: by reading this post, you hereby acknowledge that I'm just guessing and waive all right to get mad at me if you buy parts that don't fit together.

It seems a shame at all matx LGA1156 motherboards come with the GPU slot first. Most LGA775 and AM2/3 matx motherboards have it located 2nd, which gives plenty of room above and below it if the GPU is your only addon card, which is the case for a lot of matx buyers.

That could work - the Mini P180 has a huge fan on top itself. Is there an issue with drawing the hot air directly from the graphics card over the CPU cooler? I am assuming here that the fan sucks air out of the case rather than blows it in - is that true?

The First 40nm Desktop GPU .... Plus it didn't require the second slot for the cooler like the comparable nvidia 9800GTX

Make shure the cooler you buy can be mounted on a socket 1156 mainboard. The only Xigmatek model I could find is called Balder . It's prbably just rebranded HDT-S1283 with new mounting hardware. A Coolermaster Hyper 212+ will also fit and is very similar to the Xigmatek in size and performace since it's based on the heatpipe direct touch technology from Xigmatek.
Mounting the cooler towards the back of the case might be tight since the graphics card cooler exteds to the back of the card and might get in the way. Mounting for top flow should be ok.