So I am buying a new laptop soon. There are some things that I would like to get some advice on:

-I want to have a decent graphics card, which one is better AMD or nVidia in Linux? I guess all laptops come with hybrid graphics now so I also want to know which one is better when it comes to switching between discrete and integrated graphics.

-Is there a preferable brand when it comes to support for Linux? I really like Sony Vaio but if another brand is better I would choose that instead.

-Is there a distribution more suitable for laptops? I would prefer a debian or arch based distro.

-Are there any live USB distros that can be used to try hardware compatibility? Does any live USB/CD support hybrid graphics without installing so that it can be tested?

Thanks in advance!

/J

Not all laptops come with hybrid graphics, and I've had very good luck with Vaio's over the years (using one right now). I've also had better luck with nVidia graphics in Linux, too. I've heard folks have problems with the hybrid graphics, and switching can be a chore, but take that for what it's worth. I've got the VPCF1 series with the integrated nVidia. Installing the official nVidia driver from there site was no problem at all, and when I did, it automatically picked up the HDMI output, and switches/detects when I've got another monitor/TV plugged in.
Can't speak to that...I've used openSUSE for years, and I'm at 11.4 now, going to 12.2 when it comes out. Good support for all the built-in laptop gadgets, but I'm sure Deiban or Arch would work well too.
openSUSE, Fedora, and Debian all have live distros you can test with.

about hybrid graphics... it's not yet supported.
i don't think you can use NVIDIA/ATI discrete graphics with these features.

mine have hybrid graphics with no MUX. meaning no physical button and multiplexer to switch between GPU's, this is the recent design (auto switching). only software switch can switch them. you may not be able to use the high powered graphics card. for now you can only switch the discrete ones off.
but yeah the first OS i installed here in my beloved laptop was Debian with no regret whatsoever.
make sure you upgrade your debian from stable to testing or unstable to get a more recent driver support for integrated graphics(the low power one).

note: you can still enjoy compiz with intel integrated GPU^^

My laptop is half a year old. And only has an Intel HD Graphics 3000 chip build into the SandyBridge i3 2.1 GHz CPU.
Running on Linux Mint 12 with KDE. And it works like a charm. Can use nearly all special effects which are build into KDE.

Now I'm not a die hard gamer on my laptop. I have a PC for that with Windows 7. But the games I've tested so far work fine

I know that you're looking for a laptop which has both. A lowpower chip and an ATI/NVIDIA chip as well. Just wished to point out that you can get pretty much all eyecandy with the on-dye Intel Graphics.

Knoppix is the 'de facto' live distro, Debian based, usually has all firmware blobs in it.

Knoppix 7.0 out now, or very soon.

My reccomendation depends primarily on your price range. If money is not an issue, I reccomend System76. If price is important, I would reccomend either my own line which Launches in July, OR assumng you do not want to wait, InaTux. Their prices are relatively comparable to Windows machines. Plus, InaTux sell brands like Gateway, Acer & HP, not there own brand. That is a good thing as weell as a bad thing. On one hand, these are well known brands & models. On the other hand, thay are exactly the same machines you would by with Windows. No changes beyond the Windows being replaced by Linux. System76 manufactures its own line built for optimum performance with Linux. Syste76's one downfall in my view is that their prices are quite high. It is a great product, just overpriced. Oh, & as far as I know, theu will only sell them with Ubuntu Linux. If you want to use a different distro, you will need to install it yourself.
Like System76, the LPC+ TuxBook will be designed for optimum Linux performance, but will typically cost considerably less than System76 & you can have ANY Linux distro you want pre-installed!