People are either going to respect this post or I'm going to get torn to pieces.. we'll see:
I'd recommend you start with Ubuntu. To answer some of your questions, it's not the version per-se of linux but rather the distrbution. Drivers are provided by 'linux' itself.. the kernel and loadable modules provide your drivers. These drivers will be the same more or less across every different distribution (provided its linux 2.6, you will see differences in older versions like 2.4). Ubuntu does automated hardware detection and should work well for your purpose.
Now here's the part where I get eaten alive:
Keep in mind that you're going to have a slightly harder time because you're using an ATI card. I've never had a good experience with any open source operating system and ATI hardware, especially considering you want to do two screens / dual monitor. I highly recommend anyone that wants a laptop for linux purposes to try and find one with an nvidia based chipset/GPU. It'll save you so many headaches later.. if you do go the ATI/Ubuntu route be sure and read the guide at https://wiki.ubuntu.com/BinaryDriverHowto/ATI
If you have any questions I can try and help you, either post here or PM me.