Distro flavors - i386 or AMD64?

Hi all,

I am struggling to understand what distro flavor I should be using:

I have a AMD Athlon 64 x2 dual core 3800+ processor so I downloaded an amd64 version of a distro and it says that I have used an incompatible kernel when I go to load.

I have done a fair bit of searching for info on what kernels go with what processors but have not found much info - I don't think I am phrasing the question in the right way (since I don't understand the topic this not hard to get wrong). I would appreciate any pointers to resources or info as to why I am getting this message. Any other info to help me pick between the plethora of files after one has chosen a distro would be great.

And as a throw away question - what is an appliance and how is that different from a distro?

Many thanks
BB