I was wondering if the gtx 670/HD 7950 would work with the 300 watt psu. I'm aware that up to the gtx 660 ti and HD 7870 it works, I'd like to know if higher end cards will work. My preference goes to the Nvidia card.

There's a couple of concerns:

1) power draw - You don't mention your CPU or other components... If you have a 65W TDP CPU, your system might draw 115W or so running Prime 95. If it's a 95W CPU, raise this to 145W or so. That theoretically leaves 155-185W for a video card IF the supply can support nearly 300W from the 12V rail.

Video card TDP:
HD 7850 130
GTX 650 Ti 110
GTX 660 140
GTX 660 Ti 150
HD 7870 175
GTX 670 170

I'd be hesitant to put more than a HD7850 / GTX 660 in there.

2) power connectors: Do you have the 2 PEG connectors for the Video card or do you need to get some molex-> PEG adapters?

3) Single rail or multi-rail PSU design? If multi-rail, then you'd want to use connectors from more than one rail.

4) card length and fit.

5) Thermal and noise: If you opt to run the PSU near 300W, I'd expect the system to run noisy and hot. The PSU is only bronze rated, so it'll add another 60W of heat.

I've got an i5 2500k, I'll probably need a power adapter.

My pc is:
Shuttle SH67H3
i5 2500k
2x4gb ram
1 HDD
I've red about people even fitting a gtx 570, and that's a pretty long card, right.
[url]http://www.shuttle.eu/produits/mini-pc/sh67h3/specification/?L=2/\\\\\\\\[/url]
These are the specs of the barebone.