Hi.
I'm going to install debian on my new laptop HP nx6325 Sempron 3500+
the processor is an AMD Sempron 3500+ (1,8GHz) 512 KB L2-cache, 667 MHz FSB
And i don't know which kernel to install. So if someone who knows could tell me if it's k8 k7 or i686 or something else and if there is a good, understadeble list so you know what cpu goes with what kernel.

I'd guess it's i686, k8 and k7 might be more specific about which kernels they support. Actually a kernel can have built-in support for many types of kernels I think, but it's usually not neede to have more than one or two common, since probably not many people run seven systems with different kernels with one single kernel and those can build themselves a custom kernel for that.

i686 is a "generic" kernel for newer systems I think (i386 should work more generally, i686 is probably just optimized for newer systems), and should work. You may google about k7 and k8 to find out more information what they do specifically, or if you feel lucky, compile a custom kernel for yourself (it's not that difficult, but updating that kernel needs you to rebuild the new kernel again, and getting the configuration to be "good" for you might take some time first).